Question

Me ajudem nesse exercício sobre matriz: Se A= 1 2 e A (elevado a
a b
ao quadrado) = 9 -4 calcule o
-8 17
valor a+b??

Answer 1

Bom...

Pelo que entendi:

$A = \left[\begin{array}{ccc}1&2\\a&b\\\end{array}\right]$

$A^{2} = \left[\begin{array}{ccc}9&-4\\-8&17\\\end{array}\right]$

$A . A = A^{2}$

$\left[\begin{array}{ccc}1&2\\a&b\\\end{array}\right] . \left[\begin{array}{ccc}1&2\\a&b\\\end{array}\right] = \left[\begin{array}{ccc}9&-4\\-8&17\\\end{array}\right]$

$\left[\begin{array}{ccc}1.1+2.a&1.2+2.b\\a.1+a.b&2.a+b.b\\\end{array}\right] = \left[\begin{array}{ccc}9&-4\\-8&17\\\end{array}\right]$

$\left[\begin{array}{ccc}2a+1&2b+2\\a+ab& b^{2}+2a \\\end{array}\right] = \left[\begin{array}{ccc}9&-4\\-8&17\\\end{array}\right]$

2a + 1 = 9
2a = 9 - 1
2a = 8
  a = $\frac{8}{2}$
  a = 4

2b + 2 = -4
2b = - 4 - 2
2b = -6
  b = $- \frac{6}{2}$
  b = - 3

a + b = 4 - 3 = 1

Espero ter ajudado!

Boa Sorte nos Estudos! ;)