Question

Exercício sobre matrizes

Answer 1

a)

$5\cdot\left[\begin{array}{ccc}2&0&-1\\-4&1&3\end{array}\right] =\left[\begin{array}{ccc}5\cdot2&5\cdot0&5\cdot(-1)\\5\cdot(-4)&5\cdot1&5\cdot3\end{array}\right] =\left[\begin{array}{ccc}10&0&-5\\-20&5&15\end{array}\right]$

b)

$-2\cdot\left[\begin{array}{ccc}0&-1&2\\5&0&6\end{array}\right] =\left[\begin{array}{ccc}(-2)\cdot0&(-2)\cdot-1&(-2)\cdot2\\(-2)\cdot5&(-2)\cdot0&(-2)\cdot6\end{array}\right]=\left[\begin{array}{ccc}0&2&-4\\-10&0&-12\end{array}\right]$

c)

$2\cdot\left[\begin{array}{ccc}2&0&-1\\-4&1&3\end{array}\right] +3\cdot\left[\begin{array}{ccc}0&-1&2\\5&0&6\end{array}\right] =\\\\\left[\begin{array}{ccc}2\cdot2&2\cdot0&2\cdot(-1)\\2\cdot(-4)&2\cdot1&2\cdot3\end{array}\right] +\left[\begin{array}{ccc}3\cdot0&3\cdot(-1)&3\cdot2\\3\cdot5&3\cdot0&3\cdot6\end{array}\right]=\\ \\\left[\begin{array}{ccc}4&0&-2\\-8&2&6\end{array}\right] +\left[\begin{array}{ccc}0&-3&6\\15&0&18\end{array}\right]=$

$\left[\begin{array}{ccc}(4+0)&(0+(-3))&(-2+6)\\(-8+15)&(2+0)&(6+18)\end{array}\right]=\\\\\left[\begin{array}{ccc}4&-3&4\\7&2&24\end{array}\right]$