Question

Для данной матрицы: а) проставить размерность б) протранспонировать матрицу в) перемножить, если это возможно

Answer 1

$1)\; \; A=\left(\begin{array}{lll}-2&4&1\\0&5&1\end{array}\right)\; \; \; a)\; [\, 2\times 3\, ]\; \; ,\; \; b)\; \; A^{T}=\left(\begin{array}{cll}-2&0\\4&5\\1&1\end{array}\right)\\\\\\c)\; \; AF=\left(\begin{array}{lll}-2&4&1\\0&5&1\end{array}\right)\times \left(\begin{array}{l}-3\\1\\2\end{array}\right)=\left(\begin{array}{l}12\\7\end{array}\right)\\\\\\AD=\left(\begin{array}{ccc}-2&4&1\\0&5&1\end{array}\right)\times \left(\begin{array}{ll}0&3\\1&-4\\2&1\end{array}\right)=\left(\begin{array}{lll}6&-21\\7&-19\end{array}\right)$

$2)\; \; B=\left(\begin{array}{cc}1&1\\-1&0\end{array}\right)\; \; ,\; \; a)\; \; [\, 2\times 2\, ]\; \; ,\; \; b)\; \; B^{T}=\left(\begin{array}{cc}1&-1\\1&0\end{array}\right)\\\\\\BA=\left(\begin{array}{cc}1&1\\-1&0\end{array}\right)\times \left(\begin{array}{ccc}-2&4&1\\0&5&1\end{array}\right)=\left(\begin{array}{ccc}-2&9&2\\2&-4&-1\end{array}\right)$

$3)\; \; F=\left(\begin{array}{c}-3\\1\\2\end{array}\right)\; \; ,\; \; a)\; \; [\, 3\times 1\, ]\; \; ,\; \; b)\; \; F^{T}=\left(\begin{array}{ccc}-3&1&2\end{array}\right)$

$c)\; FC=\left(\begin{array}{ccc}-3\\1\\2\end{array}\right)\times \left(\begin{array}{cc}2&3\end{array}\right)=\left(\begin{array}{ccc}-6&-9\\2&3\\4&6\end{array}\right)\\\\\\4)\; \; D=\left(\begin{array}{cc}0&3\\1&-4\\2&1\end{array}\right)\; \; ,\; \; a)\; \; [\, 3\times 2\, ]\; \; ,b)\; \; D^{T}=\left(\begin{array}{ccc}0&1&2\\3&-4&1\end{array}\right)\\\\\\c)\; DB=\left(\begin{array}{ccc}0&3\\1&-4\\2&1\end{array}\right)\times \left(\begin{array}{cc}1&1\\-1&0\end{array}\right)=\left(\begin{array}{ccc}-3&0\\5&1\\1&2\end{array}\right)\\\\\\5)\; \; C=\left(\begin{array}{cc}2&3\end{array}\right)\; \; ,\; \; a)\; \; [\, 1\times 2\, ]\; \; ,\; \; b)\; \; C^{T}=\left(\begin{array}{c}2\\3\end{array}\right)$

$c)\; \; CB=\left(\begin{array}{cc}2&3\end{array}\right)\times \left(\begin{array}{cc}-1&1\\-1&0\end{array}\right)=\left(\begin{array}{cc}-5&2\end{array}\right)$