Question

Me ajude por favor!!!!!!

Dadas as matrizes

Answer 1

Explicação passo-a-passo:

A matriz transposta é aquela que se inverte as linhas pelas colunas de uma matriz dada.

Temos as seguintes matrizes:

$A=\left[\begin{array}{ccc}1&2&3\\-1&4&0\\\end{array}\right] \\\\\\\implies A^{t} =\left[\begin{array}{ccc}1&-1\\2&4\\3&0\end{array}\right]$

$B=\left[\begin{array}{ccc}2&1\\1&2\\0&4\end{array}\right] \\\\\\\implies B^{t} =\left[\begin{array}{ccc}2&1&0\\1&2&4\\\end{array}\right]$

Calculando o produto matricial:

$B^{t}.A^{t}=\left[\begin{array}{ccc}2&1&0\\1&2&4\\\end{array}\right] .\left[\begin{array}{ccc}1&-1\\2&4\\3&0\end{array}\right]\\\\\\B^{t}.A^{t}=\left[\begin{array}{ccc}2.1+1.2+0.3&2.(-1)+1.4+0.0\\1.1+2.2+4.3&1.(-1)+2.4+4.0\\\end{array}\right] \\\\\\B^{t}.A^{t}=\left[\begin{array}{ccc}2+2+0&-2+4+0\\1+4+12&-1+8+0\\\end{array}\right] \\\\\\\boxed{\boxed{B^{t}.A^{t}=\left[\begin{array}{ccc}4&2\\17&7\\\end{array}\right] }}$