<span><span>1)Выделим полный квадрат <span><span>(2<span>x21</span>+5<span>x22</span>+4<span>x1</span><span>x2</span>=2(<span>x1</span>+2<span>x1</span><span>x2</span>)+5<span>x22</span>=</span><span>(2<span>x12</span>+5<span>x22</span>+4<span>x1</span><span>x2</span>=2(<span>x1</span>+2<span>x1</span><span>x2</span>)+5<span>x22</span>=</span></span> <span><span>=(2(<span>x1</span>+<span>x2</span><span>)2</span>+3<span>x22</span>=2<span>y21</span>+3<span>y22</span></span><span>=(2(<span>x1</span>+<span>x2</span><span>)2</span>+3<span>x22</span>=2<span>y12</span>+3<span>y22</span></span></span>, преобразование <span><span><span>y1</span>=<span>x1</span>+<span>x2</span>;<span>y2</span>=<span>x2</span></span><span><span>y1</span>=<span>x1</span>+<span>x2</span>;<span>y2</span>=<span>x2</span></span></span>, выразим старые переменные через новые <span><span><span>x1</span>=<span>y1</span>−<span>y2</span>;<span>x2</span>=<span>y2</span></span><span><span>x1</span>=<span>y1</span>−<span>y2</span>;<span>x2</span>=<span>y2</span></span></span>. Матрица преобразования (1-я строка) <span><span>(1;−1)</span><span>(1;−1)</span></span>, вторая <span><span>(0;1)</span><span>(0;1)</span></span>.
</span><span>2)Запишите матрицу: 1-я строка <span><span>(2;−2;2)</span><span>(2;−2;2)</span></span>, 2-я строка <span><span>(−2;0;−4)</span><span>(−2;0;−4)</span></span>, 3-я строка <span><span>(2;−4;−3)</span><span>(2;−4;−3)</span></span>. Посчитайте главные миноры <span><span><span>Δ1</span>=2,<span>Δ2</span>=−4,<span>Δ3</span>=12</span><span><span>Δ1</span>=2,<span>Δ2</span>=−4,<span>Δ3</span>=12</span></span>, посчитайте <span><span><span><span>Δ<span>i+1</span></span><span>Δi</span></span>,<span>Δ0</span>=1</span><span><span><span>Δ<span>i+1</span></span><span>Δi</span></span>,<span>Δ0</span>=1</span></span>, получите <span><span>2<span>y21</span>−2<span>y22</span>−3<span>y23</span></span><span>2<span>y12</span>−2<span>y22</span>−3<span>y32</span></span></span>. Знаки - понятно.</span></span>
