Question

1) Considere as matrizes A, B, C e D e calcule o que se pede:​

Answer 1

Resposta:

a)  $\left[\begin{array}{ccc}3&0&-21\\4&0&-20\\7&0&-23\end{array}\right]$    b )  $\left[\begin{array}{ccc}3\\-2&\end{array}\right]$   c )  $\left[\begin{array}{ccc}-5&2\\0&0\\7&2\end{array}\right]$

Explicação passo a passo:

$B^{t}=$ matriz transposta de B

Pega-se na matriz B e as linhas passam a colunas

$B^t= \left[\begin{array}{ccc}2&0&-4\\1&0&-5\end{array}\right]$

O mesmo para a matriz A.

$A^t=\left[\begin{array}{ccc}-1&0&2\\5&4&3\end{array}\right]$

a) $A * B^t =$ $\left[\begin{array}{ccc}-1&5\\0&4\\2&3\end{array}\right]$ * $\left[\begin{array}{ccc}2&0&-4\\1&0&-5\end{array}\right]$ =

=  $\left[\begin{array}{ccc}-1*2+5*1&-1*0+5*0&-1*(-4)+5*(-5)\\0*2+4*1&0*0+4*0&0*(-4)+4*(-5)\\2*2+3*1&2*0+3*0&2*(-4)+3*(-5)\end{array}\right]$

= $\left[\begin{array}{ccc}3&0&-21\\4&0&-20\\7&0&-23\end{array}\right]$

b)

$A^t=\left[\begin{array}{ccc}-1&0&2\\5&4&3\end{array}\right]$ * $\left[\begin{array}{ccc}-1&\\0\\1\end{array}\right]$  =  $\left[\begin{array}{ccc}-1*(-1)+0*0+2*1\\5*(-1)+4*0+3*1\end{array}\right]$ = $\left[\begin{array}{ccc}3\\-2&\end{array}\right]$

c)

$\left[\begin{array}{ccc}2&1\\0&0\\-4&-5\end{array}\right]$ * $\left[\begin{array}{ccc}-3&2\\1&-2\end{array}\right]$ = $\left[\begin{array}{ccc}2*(-3)+1*1&2*2+1*(-2)\\0*(-3)+0*1&0*2+0*(-2)\\-4*(-3)-5*1&-4*2-5*(-2)\end{array}\right]$

= $\left[\begin{array}{ccc}-5&2\\0&0\\7&2\end{array}\right]$

Bons estudos.

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Símbolo : ( * ) multiplicar      $(A^t)$  matriz transposta de matriz A