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<title>A.II.4.14</title>
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<div class="feladat">
<b>Feladat: 4.14.</b><br /> <a name="a_ii_linalg_061220_ha_komb_01b" /><a href="bib_box.php?mode=sne-s-j-&amp;citation_num=" target="bib_box" onclick="mutat('bib_box.php?mode=sne-s-j-&amp;citation_num='); return false;"></a>Az alábbi két egyenletrendszer közül az egyikben az egyenletek nem

függetlenek. Válasszuk ki ezt az egyenletrendszert és fejezzük ki

az egyik egyenletet a többi lineáris kombinációjaként!

<div class="p"><!----></div>

<b>a)</b> <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mrow><m:mo> </m:mo>

<m:mtable>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mn>3</m:mn><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>4</m:mn><m:mi>y</m:mi><m:mo>+</m:mo><m:mn>7</m:mn><m:mi>z</m:mi></m:mrow></m:mtd><m:mtd columnalign="left"><m:mrow><m:mo>=</m:mo><m:mn>2</m:mn><m:mo>;</m:mo></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mn>2</m:mn><m:mi>x</m:mi><m:mo>+</m:mo><m:mi>y</m:mi><m:mo>+</m:mo><m:mn>4</m:mn><m:mi>z</m:mi></m:mrow></m:mtd><m:mtd columnalign="left"><m:mrow><m:mo>=</m:mo><m:mn>1</m:mn><m:mo>;</m:mo></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>7</m:mn><m:mi>y</m:mi><m:mo>+</m:mo><m:mn>2</m:mn><m:mi>z</m:mi></m:mrow></m:mtd><m:mtd columnalign="left"><m:mrow><m:mo>=</m:mo><m:mn>1</m:mn><m:mo>.</m:mo></m:mrow></m:mtd></m:mtr></m:mtable>

<m:mo>}</m:mo></m:mrow></m:mrow></m:math> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <b>b)</b>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mrow><m:mo> </m:mo>

<m:mtable>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mn>3</m:mn><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>4</m:mn><m:mi>y</m:mi><m:mo>+</m:mo><m:mn>7</m:mn><m:mi>z</m:mi></m:mrow></m:mtd><m:mtd columnalign="left"><m:mrow><m:mo>=</m:mo><m:mn>2</m:mn><m:mo>;</m:mo></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mn>2</m:mn><m:mi>x</m:mi><m:mo>+</m:mo><m:mi>y</m:mi><m:mo>+</m:mo><m:mn>4</m:mn><m:mi>z</m:mi></m:mrow></m:mtd><m:mtd columnalign="left"><m:mrow><m:mo>=</m:mo><m:mn>1</m:mn><m:mo>;</m:mo></m:mrow></m:mtd></m:mtr>

<m:mtr><m:mtd columnalign="right"><m:mrow><m:mo>-</m:mo><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>7</m:mn><m:mi>y</m:mi><m:mo>+</m:mo><m:mi>z</m:mi></m:mrow></m:mtd><m:mtd columnalign="left"><m:mrow><m:mo>=</m:mo><m:mn>1</m:mn><m:mo>.</m:mo></m:mrow></m:mtd></m:mtr></m:mtable>

<m:mo>}</m:mo></m:mrow></m:mrow></m:math>
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<div class="feladat">
<a name="_solution_a_ii_linalg_061220_ha_komb_01b" /><b>Megoldás: 4.14</b><br />
<b>a)</b> megoldása <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>x</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:mn>1</m:mn></m:mrow>

<m:mrow><m:mn>5</m:mn></m:mrow>

</m:mfrac>

</m:mrow></m:math>, <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>y</m:mi><m:mo>=</m:mo>

<m:mfrac><m:mrow><m:mn>2</m:mn></m:mrow>

<m:mrow><m:mn>5</m:mn></m:mrow>

</m:mfrac>

</m:mrow></m:math>, <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>z</m:mi><m:mo>=</m:mo><m:mn>0</m:mn></m:mrow></m:math>.

<b>b)</b> (3) = 3(1) - 5(2)
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