Question

1) Dada a matriz calcule A AA e, em seguida, some todos os seus termos: a) O b) 1 c) 16 d) 15 e) 32​

Answer 1

Resposta:

Explicação passo a passo:

Temos que

$A^{4}=A.A.A.A$

Então,

$A.A.A.A=\left[\begin{array}{ccc}2&0\\1&1\\\end{array}\right].\left[\begin{array}{ccc}2&0\\1&1\\\end{array}\right].\left[\begin{array}{ccc}2&0\\1&1\\\end{array}\right].\left[\begin{array}{ccc}2&0\\1&1\\\end{array}\right]=\left[\begin{array}{ccc}4&0\\3&1\\\end{array}\right].\left[\begin{array}{ccc}4&0\\3&1\\\end{array}\right]=\left[\begin{array}{ccc}16&0\\15&1\\\end{array}\right]$

Logo,

16 + 15 + 1 = 32

Alternativa e)