• Matéria: Matemática
  • Autor: Alejandra0
  • Perguntado 6 anos atrás

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:

Anexos:

Respostas

respondido por: Anônimo
2

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


Alejandra0: Obrigada!!
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