Suponha que A ≠ 0 e AB = AC onde A, B, C são matrizes tais que a multiplicação esteja definida.
a) B = C?
b) Se existir uma matriz Y, tal que YA = I, onde I é a matriz identidade, então B = C?
Explique por que, em geral, (A + B)² ≠ A² + 2AB + B² e (A + B)(A - B) ≠ A² - B².
![8. Se A é uma matriz triangular superior, então A² é __________.
9. Ache x, y, z, w se [ x y ] [ 2 3 ] = [ 1 0 ]
[ z w ] [ 3 4 ] = [ 0 1 ]
10. Dadas A = [ 1 -3 2 ] B = [ 1 4 1 ] C = [ 2 1 -1 ]
[ 2 1 -3 ] [ 2 1 1 ] [ 3 -2 -1 ]
[ 4 -3 -1 ] [ -1 2 1 ] [ 2 -5 -1 ]
mostre que AB = AC.
11. Suponha que A ≠ 0 e AB = AC onde A, B, C são matrizes tais que a multiplicação esteja definida.
a) B = C?
b) Se existir uma matriz Y, tal que YA = I, onde I é a matriz identidade, então B = C?
12. Explique por que, em geral, (A + B)² ≠ A² + 2AB + B² e (A + B)(A - B) ≠ A² - B².
13. Dadas A = [ 2 -3 -5 ] B = [ -1 3 5 ] C = [ 2 -2 -4 ]
[ -1 4 5 ] [ 1 -3 -5 ] [ -1 3 4 ]
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