Question

Sendo A=$\left[\begin{array}{ccc}1&3&5\\7&9&-1\\&&\end{array}\right]$ B= $\left[\begin{array}{ccc}6&7&0\\1&-3&-1\\&&\end{array}\right]$ C= $\left[\begin{array}{ccc}4&5&2\\-1&0&-4\\&&\end{array}\right]$ Encontre a matriz X, determinada pela expressão: X - 3A - 2B - C

Answer 1

$X=3A-2B-C$

$3A= \left[\begin{array}{ccc}3\cdot1&3\cdot3&3\cdot5\\3\cdot7&3\cdot9&3(-1)\end{array}\right] = \left[\begin{array}{ccc}3&9&15\\21&27&-3\end{array}\right]$

$2B= \left[\begin{array}{ccc}2\cdot6&2\cdot7&2\cdot0\\2\cdot1&2(-3)&2(-1)\end{array}\right] = \left[\begin{array}{ccc}12&14&0\\2&-6&-2\end{array}\right]$

$3A-2B= \left[\begin{array}{ccc}3-12&9-14&15-0\\21-2&27-(-6)&-3-(-2)\end{array}\right] = \left[\begin{array}{ccc}-9&-5&15\\19&33&-1\end{array}\right]$

$3A-2B-C= \left[\begin{array}{ccc}-9-4&-5-5&15-2\\19-(-1)&33-0&-1-(-4)\end{array}\right] = \\ \\ = \left[\begin{array}{ccc}-13&-10&13\\20&33&3\end{array}\right]$

$X= \left[\begin{array}{ccc}-13&-10&13\\20&33&3\end{array}\right]$