Question

Dadas as matrizes A= ( 2-3 e 4-1) e B=( 01 e 23) calcule 4A +5B:

Answer 1

Explicação passo-a-passo:

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Temos as seguintes matrizes:

$A=\left(\begin{array}{ccc}2&-3\\4&-1\\\end{array}\right)\ \ e \ \ B=\left(\begin{array}{ccc}0&1\\2&3\\\end{array}\right)$

Calculando 4A:

$4A=4.\left(\begin{array}{ccc}2&-3\\4&-1\\\end{array}\right)\\\\4A=\left(\begin{array}{ccc}4.2&4.(-3)\\4.4&4.(-1)\\\end{array}\right)\\\\\boxed{4A=\left(\begin{array}{ccc}8&-12\\16&-4\\\end{array}\right)}$

Calculando 5B:

$5 B=5.\left(\begin{array}{ccc}0&1\\2&3\\\end{array}\right)\\\\5 B=\left(\begin{array}{ccc}5.0&5.1\\5.2&5.3\\\end{array}\right)\\\\\boxed{5 B=\left(\begin{array}{ccc}0&5\\10&15\\\end{array}\right)}$

Calculando 4A+5B:

$4A+5B=\left(\begin{array}{ccc}8&-12\\16&-4\\\end{array}\right)+\left(\begin{array}{ccc}0&5\\10&15\\\end{array}\right)\\\\4A+5B=\left(\begin{array}{ccc}8+0&-12+5\\16+10&-4+15\\\end{array}\right)\\\\\boxed{\boxed{4A+5B=\left(\begin{array}{ccc}8&-7\\26&-11\\\end{array}\right)}}$