Question

Não entendi muito de matrizes se alguém puder me ajudar.

Answer 1

Resposta:

Explicação passo-a-passo:

$a) \left[\begin{array}{cc}5&4\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}1\\3\end{array}\right]=\left[\begin{array}{c}5\cdot 1+4\cdot 3\\-2\cdot 1+3\cdot 3\end{array}\right]=\left[\begin{array}{c}17\\7\end{array}\right]$$b) \left[\begin{array}{ccc}1&0&-2\\3&2&0\\1&4&-3\end{array}\right] \cdot \left[\begin{array}{c}-2\\0\\5\end{array}\right]=\left[\begin{array}{c}1\cdot (-2)+0\cdot 0+(-2)\cdot 5\\3\cdot (-2)+2\cdot 0+0\cdot 5\\1\cdot (-2)+4\cdot 0+(-3)\cdot 5\end{array}\right]=\left[\begin{array}{c}-12\\-6\\-16\end{array}\right]$$c) \left[\begin{array}{ccc}2&4&-2\end{array}\right] \cdot \left[\begin{array}{c}0\\2\\-2\end{array}\right] =\left[\begin{array}{c}12\cdot 0+4\cdot 2+(-2)\cdot(-2)\end{array}\right] =\left[\begin{array}{c}12\end{array}\right]$$d) \left[\begin{array}{c}2\\0\\3\\-1\end{array}\right] \cdot \left[\begin{array}{cccc}0&2&-1&5\end{array}\right] =\left[\begin{array}{cccc}2\cdot 0&2\cdot 2&2\cdot(-1)&2\cdot 5\\0\cdot 0&0\cdot 2&0\cdot(-1)&0\cdot 5\\3\cdot 0&3\cdot 2&3\cdot(-1)&3\cdot 5\\(-1)\cdot 0&(-1)\cdot 2&(-1)\cdot(-1)&(-1)\cdot 5\end{array}\right] =\left[\begin{array}{cccc}0&4&-2&10\\0&0&0&0\\0&6&-3&15\\0&-2&1&-5\end{array}\right]$