Question

determine a, b, x, e y para que as matrizes

( x+y 2a+b 2a+b ) ( 3 -1 )
| | | |
( 2x-y a-b a-b ) ( 0 7 )

sejam iguais :
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Answer 1

\begin{gathered} A =\left[\begin{array}{ccc}x+y&2a+b&\\&&\\2x-y&a-b&\end{array}\right] \\ \\ B= \left[\begin{array}{ccc}3&0&\\&&\\-1&-7&\end{array}\right] \end{gathered}

A=

⎣

⎢

⎡

x+y

2x−y

2a+b

a−b

⎦

⎥

⎤

B=

⎣

⎢

⎡

3

−1

0

−7

⎦

⎥

⎤

Se as matrizes são iguais

x + y = 3 2a + b = 0

2x - y = - 1 a - b = - 7

Resolvendo os sistemas

x = 2/3 a = - 7/3

y = 7/3 b = 14/3