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<Text-field style="Text" size="18" bold="true" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" size="18">\316\225\317\201\316\263\316\261\317\203\317\204\316\256\317\201\316\271\316\277 \316\234\316\261\316\270\316\267\316\274\316\261\317\204\316\271\316\272\317\216\316\275</Font></Text-field>
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<Text-field style="Text" size="18" bold="true" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" size="18">\316\223\316\265\316\275\316\271\316\272\317\214 \316\244\316\274\316\256\316\274\316\261 \316\223\316\265\316\275\316\271\316\272\317\216\316\275 \316\234\316\261\316\270\316\267\316\274\316\254\317\204\317\211\316\275</Font></Text-field>
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<Input>
<Text-field style="Text" size="18" bold="true" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" size="18">\316\221.\316\243.\316\240\316\221\316\231.\316\244\316\225.</Font></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
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<Text-field style="Text" size="14" bold="true" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" foreground="[255,0,0]" size="14">3\316\277 \316\225\317\201\316\263\316\261\317\203\317\204\316\267\317\201\316\271\316\277 </Font></Text-field>
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<Input>
<Text-field style="Text" size="14" bold="true" layout="Normal" alignment="centred"><Font bold="false" encoding="UTF-8" size="14">\316\231\316\264\316\271\316\277\317\204\316\271\316\274\316\255\317\202- \316\231\316\264\316\271\316\277\316\264\316\271\316\261\316\275\317\215\317\203\316\274\316\261\317\204\316\261</Font></Text-field>
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<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font encoding="UTF-8" size="14">\316\225\316\271\316\264\316\271\316\272\316\255\317\202 \316\274\316\256\317\204\317\201\316\265\317\202, \316\265\317\215\317\201\316\265\317\203\316\267 \316\271\316\264\316\271\316\277\317\204\316\271\316\274\317\216\316\275 \316\272\316\261\316\271 \316\271\316\264\316\271\316\277\316\264\316\271\316\261\316\275\317\205\317\203\316\274\316\254\317\204\317\211\316\275.</Font></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"></Text-field>
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<Text-field style="Text" size="10" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" size="10">\316\235. \316\234\316\261\317\204\316\266\316\254\316\272\316\277\317\202 </Font></Text-field>
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<Input>
<Text-field style="Text" size="10" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8" size="10">\316\225\317\200. \316\232\316\261\316\270\316\267\316\263\316\267\317\204\316\256\317\202 \316\221.\316\243.\316\240\316\221\316\231.\316\244\316\225.</Font></Text-field>
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<Input>
<Text-field style="Text" size="10" layout="Normal" alignment="centred"><Font bold="true" size="10">nikmatz@aspete.gr</Font></Text-field>
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<Text-field style="Text" size="20" bold="true" family="Book Antiqua" layout="Normal" alignment="centred"></Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">1\316\267 \316\206\317\203\316\272\316\267\317\203\316\267</Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\224\316\257\316\275\316\265\317\204\316\265 \316\267 \316\274\316\256\317\204\317\201\316\261   <Image height="76" width="118" zoomable="false"> <Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlIT0iRiotJS5CT1VORFNfSEVJR0hURzYjJCIkZyhGKi0lKUNISUxEUkVORzYi</Drawing-Root></Image></Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\235\316\261 \316\262\317\201\316\265\316\270\316\277\317\215\316\275 :</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">a.\317\204\316\277 \317\207\316\261\317\201\316\261\316\272\317\204\316\267\317\201\316\271\317\203\317\204\316\271\316\272\317\214 \317\200\316\277\316\273\317\205\317\216\316\275\317\205\316\274\316\277 \317\204\316\267\317\202 \316\221</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">b.\316\277\316\271 \316\271\316\264\316\271\316\277\317\204\316\271\316\274\316\255\317\202 \317\204\316\267\317\202 \316\221</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">c.\317\204\316\261 \316\271\316\264\316\271\316\277\316\264\316\271\316\261\316\275\317\215\317\203\316\274\316\261\317\204\316\261 \317\204\316\267\317\202 \316\221. </Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">d.\316\274\316\271\316\261 \316\264\316\271\316\261\316\263\317\211\316\275\316\277\317\200\316\277\316\257\316\267\317\203\316\267 \317\204\316\267\317\202 \316\221.</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Normal" layout="Normal"></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;</Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\246\316\277\317\201\317\204\317\216\316\275\316\277\317\205\316\274\316\265 \317\204\316\277 \317\200\316\261\316\272\316\255\317\204\316\277 \316\265\316\275\317\204\316\277\316\273\317\216\316\275 LinearAlgebra</Font></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(LinearAlgebra):</Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\237\317\201\316\257\316\266\316\277\317\205\316\274\316\265 \317\204\316\267\316\275 \316\274\316\256\317\204\317\201\316\261 \316\221</Font></Text-field>
</Input>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A:=&lt;&lt;1,1,-1&gt;|&lt;2,2,1&gt;|&lt;2,-1,4&gt;&gt;;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" "> </Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\245\317\200\316\277\316\273\316\277\316\263\316\257\316\266\316\277\317\205\316\274\316\265 \317\204\316\277 \317\207\316\261\317\201\316\261\316\272\317\204\316\267\317\201\316\271\317\203\317\204\316\271\316\272\317\214 \317\200\316\277\316\273\317\205\317\216\316\275\317\205\316\274\316\277</Font></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p:=CharacteristicPolynomial(A,x);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" ">LCoiIiohIiIqJClJInhHNiIiIiQiIiJGKiomIiIoRiopRiciIiNGKkYkKiYiIzpGKkYnRipGKg==</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\245\317\200\316\277\316\273\316\277\316\263\316\257\316\266\316\277\317\205\316\274\316\265 \317\204\316\271\317\202 \316\271\316\264\316\271\316\277\317\204\316\271\316\274\316\255\317\202, \316\273\317\215\316\275\316\277\316\275\317\204\316\261\317\202 \317\204\316\267\316\275 \317\207\316\261\317\201\316\261\316\272\317\204\316\267\317\201\316\271\317\203\317\204\316\271\316\272\316\256 \316\265\316\276\316\257\317\203\317\211\317\203\316\267</Font></Text-field>
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<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(p=0,x);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiUiIiIiIiRGJA==</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\245\317\200\316\277\316\273\316\277\316\263\316\257\316\266\316\277\317\205\316\274\316\265 \317\204\316\271\317\202 \316\271\316\264\316\271\316\277\317\204\316\271\316\274\316\255\317\202 \316\274\316\265 \317\207\317\201\316\256\317\203\316\267 \317\204\316\267\317\202 \316\265\316\275\317\204\316\277\316\273\316\256\317\202 Eigenvalues</Font></Text-field>
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<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eigenvalues(A);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" "> </Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\245\317\200\316\277\316\273\316\277\316\263\316\257\316\266\316\277\317\205\316\274\316\265 \316\271\316\264\316\271\316\277\317\204\316\271\316\274\316\255\317\202 \316\272\316\261\316\271 \316\271\316\264\316\271\316\277\316\264\316\271\316\261\316\275\317\215\317\203\316\274\316\261\317\204\316\261</Font></Text-field>
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<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">l,P:=Eigenvectors(A);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" "> </Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\227 \316\264\316\271\316\261\316\263\317\216\316\275\316\271\316\261 \316\274\316\256\317\204\317\201\316\261 \316\265\316\257\316\275\316\261\316\271:</Font></Text-field>
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<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Diag:=Matrix(1..3,1..3,l,shape = diagonal);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" "> </Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\240\317\201\316\254\316\263\316\274\316\261\317\204\316\271:</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P.Diag.MatrixInverse(P);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" "> </Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\227 \316\264\316\271\316\261\316\263\317\216\316\275\316\271\316\261 \316\274\316\265 \317\207\317\201\316\256\317\203\316\267 \317\204\316\267\317\202 \316\265\316\275\317\204\316\277\316\273\316\256\317\202 </Font>JordanForm</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">JordanForm(A);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" "> </Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
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</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">2\316\267 \316\206\317\203\316\272\316\267\317\203\316\267  </Font></Text-field></Title>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\224\316\257\316\275\316\265\317\204\316\265 \316\267 \316\274\316\256\317\204\317\201\316\261   <Image height="76" width="117" zoomable="false"> <Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIlcTZGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiRnKEYqLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image></Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\316\235\316\261 \316\262\317\201\316\265\316\270\316\277\317\215\316\275 :</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">a.\317\204\316\277 \317\207\316\261\317\201\316\261\316\272\317\204\316\267\317\201\316\271\317\203\317\204\316\271\316\272\317\214 \317\200\316\277\316\273\317\205\317\216\316\275\317\205\316\274\316\277 \317\204\316\267\317\202 \316\221</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">b.\316\277\316\271 \316\271\316\264\316\271\316\277\317\204\316\271\316\274\316\255\317\202 \317\204\316\267\317\202 \316\221</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">c.\317\204\316\261 \316\271\316\264\316\271\316\277\316\264\316\271\316\261\316\275\317\215\317\203\316\274\316\261\317\204\316\261 \317\204\316\267\317\202 \316\221. </Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">d.\316\274\316\271\316\261 \316\264\316\271\316\261\316\263\317\211\316\275\316\277\317\200\316\277\316\257\316\267\317\203\316\267 \317\204\316\267\317\202 \316\221.</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart;</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(LinearAlgebra):</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">B:=&lt;&lt;1,-1,-1&gt;|&lt;1,3,2&gt;|&lt;-1,-1,0&gt;&gt;;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" "> </Equation></Text-field>
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</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p:=CharacteristicPolynomial(B,x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" ">LCoiIiMhIiIqJClJInhHNiIiIiQiIiJGKiomIiIlRiopRidGI0YqRiQqJiIiJkYqRidGKkYq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(p=0,x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiUiIiMiIiJGJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eigenvalues(B);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" ">LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqW3k5Jj0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">l,P:=Eigenvectors(B);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display=" "> </Equation></Text-field>
</Output>
</Group>
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