Question

ALGUÉM ME AJUDA PFV!!!!​

Answer 1

Explicação passo-a-passo:

Temos as matrizes:

$A=\left[\begin{array}{ccc}-1&3\\2&-8\\\end{array}\right] \\\\B=\left[\begin{array}{ccc}2&-1\\3&0\\\end{array}\right]$

a)

$detA=(-1).(-8)-3.2\\\\detA=8-6\\\\detA=2$

b)

$detB=2.0-(-1).3\\\\detB=0+3\\\\detB=3$

c)Calculando A+B:

$A+B=\left[\begin{array}{ccc}-1&3\\2&-8\\\end{array}\right] +\left[\begin{array}{ccc}2&-1\\3&0\\\end{array}\right] \\\\A+B=\left[\begin{array}{ccc}-1+2&3+(-1)\\2+3&-8+0\\\end{array}\right] \\\\A+B=\left[\begin{array}{ccc}1&2\\5&-8\\\end{array}\right]$

Calculando o determinante:

$det(A+B)=1.(-8)-2.5\\\\det(A+B)=-8-10\\\\det(A+B)=-18$

d)Calculando A.B:

$A.B=\left[\begin{array}{ccc}-1&3\\2&-8\\\end{array}\right] .\left[\begin{array}{ccc}2&-1\\3&0\\\end{array}\right] \\\\A.B=\left[\begin{array}{ccc}(-1).2+3.3&(-1).(-1)+3.0\\2.2+(-8).3&2.(-1)+(-8).0\\\end{array}\right]\\\\A.B=\left[\begin{array}{ccc}-2+9&1+0\\4-24&-2+0\\\end{array}\right]\\\\A.B=\left[\begin{array}{ccc}7&1\\-20&-2\\\end{array}\right]$

Calculando o determinante:

$det(A.B)=7.(-2)-1.(-20)\\\\det(A.B)=-14+20\\\\det(A.B)=6$

e)Usando os valores calculado nos itens a e b:

$detA.detB=2.3\\\\detA.detB=6$