Question

sejam as matrizes

a) -1 0
2 1

b) 1 2
0 3

c) -2 0
3 2

calcule:

a) 2a + b

b) 2.at - c

c) a.b+c​

Answer 1

$\mathrm{Sejam\ as\ matrizes}\ A,\ B\ \text{e}\ C\ \text{tais que:}$

$A=\left[\begin{array}{cc}-1&0\\2&1\end{array}\right],\ B=\left[\begin{array}{cc}1&2\\0&3\end{array}\right] \ \text{e}\ C=\left[\begin{array}{cc}-2&0\\3&2\end{array}\right] .$

$\mathbf{a)}\ 2A+B$

$\Longrightarrow 2A+B=2\left[\begin{array}{cc}-1&0\\2&1\end{array}\right] +\left[\begin{array}{cc}1&2\\0&3\end{array}\right]$

$\Longrightarrow 2A+B=\left[\begin{array}{cc}-2+1&0+2\\4+0&2+3\end{array}\right]$

$\Longrightarrow \boxed{2A+B=\left[\begin{array}{cc}-1&2\\4&5\end{array}\right]}$

$\mathbf{b)}\ 2A^t-C$

$\Longrightarrow 2A^t-C=2\left[\begin{array}{cc}-1&2\\0&1\end{array}\right]-\left[\begin{array}{cc}-2&0\\3&2\end{array}\right]$

$\Longrightarrow 2A^t-C=\left[\begin{array}{cc}-2-(-2)&4-0\\0-3&2-2\end{array}\right]$

$\Longrightarrow \boxed{2A^t-C=\left[\begin{array}{cc}0&4\\-3&0\end{array}\right]}$

$\mathbf{c)}\ AB+C$

$\Longrightarrow AB+C=\left[\begin{array}{cc}-1&0\\2&1\end{array}\right]\left[\begin{array}{cc}1&2\\0&3\end{array}\right]+\left[\begin{array}{cc}-2&0\\3&2\end{array}\right]$

$\Longrightarrow AB+C=\left[\begin{array}{cc}-1+0&-2+0\\2+0&4+3\end{array}\right]+\left[\begin{array}{cc}-2&0\\3&2\end{array}\right]$

$\Longrightarrow AB+C=\left[\begin{array}{cc}-1+(-2)&-2+0\\2+3&7+2\end{array}\right]$

$\Longrightarrow\boxed{AB+C=\left[\begin{array}{cc}-3&-2\\5&9\end{array}\right]}$