Question

Dadas as matrizes determine os elementos da matriz C, de modo que a equação matricial C + 2A – B = 0 seja satisfeita.​​​​​​

Answer 1

Explicação passo-a-passo:

C+2A-B=0

C= -2A+B

-2A= -2 0

-4 2

C= -2 0. +. 2 -2

-4 2 4 5

C= 0 -2

0 7

Answer 2

Resposta:

A resposta é $\left[\begin{array}{ccc}0&2\\0&7\end{array}\right]$

Explicação passo-a-passo:

$A=\left[\begin{array}{ccc}1&0\\2&-1\end{array}\right] \\B=\left[\begin{array}{ccc}2&-2\\4&5\end{array}\right]$

C = ? se C + 2A - B = 0?

$C=\left[\begin{array}{ccc}C_{11}&C_{12} \\C_{21}&C_{22}\end{array}\right] entao\\\\C+2A-B=0\\\\\left[\begin{array}{ccc}C_{11}&C_{12} \\C_{21}&C_{22}\end{array}\right] + \left[\begin{array}{ccc}2&0\\4&2\end{array}\right] + \left[\begin{array}{ccc}-2&2\\-4&-5\end{array}\right] = \left[\begin{array}{ccc}0&0\\0&0\end{array}\right] =>$

 $\left[\begin{array}{ccc}C_{11}+2-2&C_{12}+0+2\\C_{21}+4-4 &C_{22}-2-5\end{array}\right] = \left[\begin{array}{ccc}0&0\\0&0\end{array}\right] =>$

 $\left[\begin{array}{ccc}C_{11} &C_{12} +2\\C_{21}&C_{22}-7 \end{array}\right] = \left[\begin{array}{ccc}0&0\\0&0\end{array}\right] =>$

 $C_{11} = 0\\C_{12} +2=0\\C_{21} =0 \\C_{22} -7=0$

*Passando tudo para os seus devidos lugares, fica:

$C_{11} = 0\\C_{12} = -2\\C_{21} =0\\C_{22} = 7\\\\ou => \left[\begin{array}{ccc}0&-2\\0&7\end{array}\right]$