Question

Dadas as matrizes A = [-3 4 0 2], B = [ 1 1 -1 1] e C [1 3 4 2] a matriz X tal que X + 3A - B = 2C é:

Answer 1

Explicação passo-a-passo:

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

$X+3A-B=2C$

Chamando a matriz X de   $\left[\begin{array}{ccc}x_{11}&x_{12}\\x_{21}&x_{22}\\\end{array}\right]$  , fica

$\left[\begin{array}{ccc}x_{11}&x_{12}\\x_{21}&x_{22}\\\end{array}\right]+3.\left[\begin{array}{ccc}-3&4\\0&2\\\end{array}\right]-\left[\begin{array}{ccc}1&1\\-1&1\\\end{array}\right]=2.\left[\begin{array}{ccc}1&3\\4&2\\\end{array}\right]$

$\left[\begin{array}{ccc}x_{11}&x_{12}\\x_{21}&x_{22}\\\end{array}\right]+\left[\begin{array}{ccc}3.(-3)&3.4\\3.0&3.2\\\end{array}\right]-\left[\begin{array}{ccc}1&1\\-1&1\\\end{array}\right]=\left[\begin{array}{ccc}2.1&2.3\\2.4&2.2\\\end{array}\right]$

$\left[\begin{array}{ccc}x_{11}&x_{12}\\x_{21}&x_{22}\\\end{array}\right]+\left[\begin{array}{ccc}-9&12\\0&6\\\end{array}\right]-\left[\begin{array}{ccc}1&1\\-1&1\\\end{array}\right]=\left[\begin{array}{ccc}2&6\\8&4\\\end{array}\right]$

$\left[\begin{array}{ccc}x_{11}&x_{12}\\x_{21}&x_{22}\\\end{array}\right]+\left[\begin{array}{ccc}-9-1&12-1\\0-(-1)&6-1\\\end{array}\right]=\left[\begin{array}{ccc}2&6\\8&4\\\end{array}\right]$

$\left[\begin{array}{ccc}x_{11}&x_{12}\\x_{21}&x_{22}\\\end{array}\right]+\left[\begin{array}{ccc}-10&11\\1&5\\\end{array}\right]=\left[\begin{array}{ccc}2&6\\8&4\\\end{array}\right]$

$\left[\begin{array}{ccc}x_{11}+(-10)&x_{12}+11\\x_{21}+1&x_{22}+5\\\end{array}\right]=\left[\begin{array}{ccc}2&6\\8&4\\\end{array}\right]$

$x_{11}-10=2$  →  $x_{11}=2+10$  →  $x_{11}=12$

$x_{12}+11=6$  →  $x_{12}=6-11$  →  $x_{12}=-5$

$x_{21}+1=8$  →  $x_{21}=8-1$  →  $x_{21}=7$

$x_{22}+5=4$  →  $x_{22}=4-5$  →  $x_{22}=-1$

Então, a matriz X será

    $X=\left[\begin{array}{ccc}12&-5\\7&-1\\\end{array}\right]$

Opção 1