Question

??????
Sendo A = 2 1 3 2 e B = 1 3 -2 5 , determine :
a ) A x B
b ) B x A

Answer 1

Explicação passo-a-passo:

a)

$\sf A\times B=\Big(\begin{array}{cc} \sf 2 & \sf 1 \\ \sf 3 & \sf 2 \end{array}\Big)\cdot\Big(\begin{array}{cc} \sf 1 & \sf 3 \\ \sf -2 & \sf 5 \end{array}\Big)$

$\sf A\times B=\Big(\begin{array}{cc} \sf 2\cdot1+1\cdot(-2) & \sf 2\cdot3+1\cdot5 \\ \sf 3\cdot1+2\cdot(-2) & \sf 3\cdot3+2\cdot5 \end{array}\Big)$

$\sf A\times B=\Big(\begin{array}{cc} \sf 2-2 & \sf 6+5 \\ \sf 3-4 & \sf 9+10 \end{array}\Big)$

$\sf A\times B=\Big(\begin{array}{cc} \sf 0 & \sf 11 \\ \sf -1 & \sf 19 \end{array}\Big)$

b)

$\sf B\times A=\Big(\begin{array}{cc} \sf 1 & \sf 3 \\ \sf -2 & \sf 5 \end{array}\Big)\cdot\Big(\begin{array}{cc} \sf 2 & \sf 1 \\ \sf 3 & \sf 2 \end{array}\Big)$

$\sf B\times A=\Big(\begin{array}{cc} \sf 1\cdot2+3\cdot3 & \sf 1\cdot1+3\cdot2 \\ \sf (-2)\cdot2+5\cdot3 & \sf (-2)\cdot1+5\cdot2 \end{array}\Big)$

$\sf B\times A=\Big(\begin{array}{cc} \sf 2+9 & \sf 1+6 \\ \sf -4+15 & \sf -2+10 \end{array}\Big)$

$\sf B\times A=\Big(\begin{array}{cc} \sf 11 & \sf 7 \\ \sf 11 & \sf 8 \end{array}\Big)$