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size="10">Д.з., часть 1.</f> </text> </region> <region region-id="2" left="48" top="57" width="448.5" height="34.5" align-x="48" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Пусть в пространстве </f> <f family="Arial Cyr" charset="204" size="12"> R </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> задан произвольный базис векторов </f> <f family="Arial Cyr" charset="204" size="12">(</f> <f family="Arial Cyr" charset="204" size="12"> f </f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12">,</f> <f family="Arial Cyr" charset="204" size="12"> f </f> <f family="Arial Cyr" charset="204" size="12">2</f> <f family="Arial Cyr" charset="204" size="12">,..., </f> <f family="Arial Cyr" charset="204" size="12"> f </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">), которые</f> <f family="Arial Cyr" charset="204" size="12">ниже записаны в строки матрицы </f> <f family="Arial Cyr" charset="204" size="12"> f </f> <f family="Arial Cyr" charset="204" size="12"> .</f> </text> </region> <region region-id="74" left="96" top="101.25" width="100.5" height="78.75" align-x="107.25" align-y="144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">f</ml:id> <ml:matrix rows="4" cols="4"> <ml:real>2</ml:real> <ml:real>7</ml:real> <ml:real>1</ml:real> <ml:real>5</ml:real> <ml:real>1</ml:real> <ml:real>4</ml:real> <ml:real>1</ml:real> <ml:real>7</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> <ml:real>-6</ml:real> <ml:real>7</ml:real> 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show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Построим в этом же пространстве ортогональный базис векторов {</f> <f family="Arial Cyr" charset="204" size="12"> е </f> <f family="Arial Cyr" charset="204" size="12"> k </f> <f family="Arial Cyr" charset="204" size="12">}, которые</f> <f family="Arial Cyr" charset="204" size="12">также запишем в строки матрицы </f> <f family="Arial Cyr" charset="204" size="12"> Е </f> <f family="Arial Cyr" charset="204" size="12">. </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal">Процесс ортогонализации Шмидта представ-</inlineAttr> </f> <inlineAttr font-weight="normal"> <f family="Arial Cyr" charset="204" size="12">лен в виде алгоритма. </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">Число ортогональных векторов </f> <f family="Arial Cyr" 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</ml:matrix> </result> </ml:eval> </math> <rendering item-idref="12"/> </region> <region region-id="55" left="66" top="708.75" width="265.5" height="13.5" align-x="66" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Проверим ортогональность полученного базиса:</f> </text> </region> <region region-id="64" left="66" top="744.75" width="33" height="15.75" align-x="82.5" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">w</ml:id> <ml:real>3</ml:real> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="63" left="114" top="744.75" width="30" height="15.75" align-x="127.5" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">v</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="65" left="186" top="729.75" width="117" height="50.25" align-x="281.25" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">E</ml:id> <ml:sequence> <ml:id xml:space="preserve">w</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">E</ml:id> <ml:sequence> <ml:id xml:space="preserve">v</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="15"/> </region> <region region-id="67" left="66" top="798" width="408" height="41.25" align-x="66" align-y="810" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Что и требовалось показать. Легко решает задачи 4.67 и др. при любом </f> <f family="Arial Cyr" charset="204" size="12"> q </f> <f family="Arial Cyr" charset="204" size="12">. </f> <f family="Arial Cyr" charset="204" size="12">Однако задачу с нулем 4.70 не решает. 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is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="false" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="96" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="1" left="66" top="18.75" width="214.5" height="26.25" align-x="66" align-y="30" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12"> Процесс ортогонализации Шмидта </f> <f family="Arial Cyr" charset="204" size="12">.</f> <f family="Arial Cyr" charset="204" size="10">Д.з., часть 1.</f> </text> </region> <region region-id="2" left="48" top="57" width="448.5" height="34.5" align-x="48" align-y="72" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Пусть в пространстве </f> <f family="Arial Cyr" charset="204" size="12"> R </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12"> задан произвольный базис векторов </f> <f family="Arial Cyr" charset="204" size="12">(</f> <f family="Arial Cyr" charset="204" size="12"> f </f> <f family="Arial Cyr" charset="204" size="12"> 1 </f> <f family="Arial Cyr" charset="204" size="12">,</f> <f family="Arial Cyr" charset="204" size="12"> f </f> <f family="Arial Cyr" charset="204" size="12">2</f> <f family="Arial Cyr" charset="204" size="12">,..., </f> <f family="Arial Cyr" charset="204" size="12"> f </f> <f family="Arial Cyr" charset="204" size="12"> n </f> <f family="Arial Cyr" charset="204" size="12">), которые</f> <f family="Arial Cyr" charset="204" size="12">ниже записаны в строки матрицы </f> <f family="Arial Cyr" charset="204" size="12"> f </f> <f family="Arial Cyr" charset="204" size="12"> .</f> </text> </region> <region region-id="74" left="96" top="101.25" width="100.5" height="78.75" align-x="107.25" align-y="144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">f</ml:id> <ml:matrix rows="4" cols="4"> <ml:real>2</ml:real> <ml:real>7</ml:real> <ml:real>1</ml:real> <ml:real>5</ml:real> <ml:real>1</ml:real> <ml:real>4</ml:real> <ml:real>1</ml:real> <ml:real>7</ml:real> <ml:real>3</ml:real> <ml:real>3</ml:real> <ml:real>-6</ml:real> <ml:real>7</ml:real> <ml:real>-1</ml:real> <ml:real>-3</ml:real> <ml:real>0</ml:real> <ml:real>8</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="18" left="42" top="138.75" width="30" height="15.75" align-x="55.5" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">n</ml:id> <ml:real>4</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="24" left="240" top="138.75" width="48.75" height="17.25" align-x="267" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="4"/> </region> <region region-id="25" left="330" top="107.25" width="62.25" height="78.75" align-x="354" align-y="150" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:matcol/> <ml:id xml:space="preserve">f</ml:id> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="4" cols="1"> <ml:real>2</ml:real> <ml:real>7</ml:real> <ml:real>1</ml:real> <ml:real>5</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="5"/> </region> <region region-id="53" left="48" top="198" width="473.25" height="60" align-x="48" align-y="210" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Построим в этом же пространстве ортогональный базис векторов {</f> <f family="Arial Cyr" charset="204" size="12"> е </f> <f family="Arial Cyr" charset="204" size="12"> k </f> <f family="Arial Cyr" charset="204" size="12">}, которые</f> <f family="Arial Cyr" charset="204" size="12">также запишем в строки матрицы </f> <f family="Arial Cyr" charset="204" size="12"> Е </f> <f family="Arial Cyr" charset="204" size="12">. </f> <f family="Arial Cyr" charset="204" size="12"> <inlineAttr font-weight="normal">Процесс ортогонализации Шмидта представ-</inlineAttr> </f> <inlineAttr font-weight="normal"> <f family="Arial Cyr" charset="204" size="12">лен в виде алгоритма. </f> </inlineAttr> <f family="Arial Cyr" charset="204" size="12">Число ортогональных векторов </f> <f family="Arial Cyr" charset="204" size="12">q</f> <f family="Arial Cyr" charset="204" size="12"> можно задавать произ- вольно, монотонно увеличивая его до появления в матрице </f> <f family="Arial Cyr" charset="204" size="12"> Е </f> <f family="Arial Cyr" charset="204" size="12"> нулевой строки.</f> </text> </region> <region region-id="96" left="60" top="270.75" width="30.75" height="15.75" align-x="74.25" align-y="282" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">q</ml:id> <ml:real>3</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="89" left="48" top="300.75" width="213" height="13.5" align-x="48" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Выберем произвольно первый вектор:</f> </text> </region> <region region-id="90" left="288" top="300.75" width="42" height="15.75" align-x="298.5" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="91" left="354" top="300.75" width="54" height="17.25" align-x="381" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIConstant" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">e</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:id xml:space="preserve">i</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:id xml:space="preserve">i</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="92" left="438" top="300.75" width="51" height="17.25" align-x="467.25" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">e</ml:id> <ml:sequence> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> <rendering item-idref="9"/> </region> <region region-id="94" left="48" top="330" width="371.25" height="17.25" align-x="48" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Остальные векторы<sp count="2"/> </f> <f family="Arial Cyr" charset="204" size="12">{</f> <f family="Arial Cyr" charset="204" size="12"> Е </f> <f family="Arial Cyr" charset="204" size="12"> k </f> <f family="Arial Cyr" charset="204" size="12">}</f> <f family="Arial Cyr" charset="204" size="12"> <sp count="2"/>определяются по следующему алгоритму.</f> </text> </region> <region region-id="41" left="60" top="360.75" width="287.25" height="165.75" align-x="75" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:program> <ml:for> <ml:id xml:space="preserve">k</ml:id> <ml:range> <ml:real>2</ml:real> <ml:id xml:space="preserve">q</ml:id> </ml:range> <ml:for> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>1</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:range> <ml:localDefine> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">e</ml:id> <ml:sequence> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">s</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">m</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">f</ml:id> <ml:sequence> <ml:id xml:space="preserve">k</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">e</ml:id> <ml:sequence> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">m</ml:id> </ml:boundVars> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">e</ml:id> <ml:sequence> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">m</ml:id> </ml:sequence> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">e</ml:id> <ml:sequence> <ml:id xml:space="preserve">s</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">k</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:bounds> </ml:apply> </ml:apply> </ml:localDefine> </ml:for> </ml:for> <ml:id xml:space="preserve">e</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="75" left="78" top="555.75" width="104.25" height="57.75" align-x="93" align-y="588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:symEval style="default" hide-keywords="false" hide-lhs="false" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">E</ml:id> <ml:symResult> <ml:matrix rows="3" cols="4"> <ml:real>2</ml:real> <ml:real>3</ml:real> <ml:real>0</ml:real> <ml:real>1</ml:real> <ml:real>2</ml:real> <ml:real>0</ml:real> <ml:real>3</ml:real> <ml:real>-3</ml:real> <ml:real>0</ml:real> <ml:real>-1</ml:real> <ml:real>-1</ml:real> <ml:real>0</ml:real> </ml:matrix> </ml:symResult> </ml:symEval> </math> <rendering item-idref="11"/> </region> <region region-id="76" left="288" top="557.25" width="90" height="78.75" align-x="333" align-y="600" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:matcol/> <ml:parens> <ml:apply> <ml:transpose/> <ml:id xml:space="preserve">E</ml:id> </ml:apply> </ml:parens> <ml:real>1</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:matrix rows="4" cols="1"> <ml:real>2</ml:real> <ml:real>1</ml:real> <ml:real>3</ml:real> <ml:real>-1</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="12"/> </region> <region region-id="55" left="66" top="708.75" width="265.5" height="13.5" align-x="66" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f family="Arial Cyr" charset="204" size="12">Проверим ортогональность полученного базиса:</f> </text> </region> <region region-id="64" left="66" top="744.75" width="33" height="15.75" align-x="82.5" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">w</ml:id> <ml:real>3</ml:real> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="63" left="114" top="744.75" width="30" height="15.75" align-x="127.5" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">v</ml:id> <ml:real>2</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="65" left="186" top="729.75" width="117" height="50.25" align-x="281.25" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:summation/> <ml:lambda> <ml:boundVars> <ml:id xml:space="preserve">j</ml:id> </ml:boundVars> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">E</ml:id> <ml:sequence> <ml:id xml:space="preserve">w</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:sequence> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">E</ml:id> <ml:sequence> <ml:id xml:space="preserve">v</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:sequence> </ml:apply> </ml:apply> </ml:parens> </ml:lambda> <ml:bounds> <ml:real>1</ml:real> <ml:id xml:space="preserve">n</ml:id> </ml:bounds> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> <rendering item-idref="15"/> </region> <region region-id="67" left="66" top="798" width="408" height="41.25" align-x="66" align-y="810" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial Cyr" charset="204" size="12">Что и требовалось показать. Легко решает задачи 4.67 и др. при любом </f> <f family="Arial Cyr" charset="204" size="12"> q </f> <f family="Arial Cyr" charset="204" size="12">. </f> <f family="Arial Cyr" charset="204" size="12">Однако задачу с нулем 4.70 не решает. 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