Question

Se A=[0 1] [3 2] e B= [-1 1] [0 1] , verifique que (A.B)T = BT .AT

Answer 1

Resposta: Vamos ver se os dois lados da equação são iguais:

$(AB)^T=\left(\left[\begin{array}{cc}0&1\\3&2\end{array}\right]\left[\begin{array}{cc}-1&1\\0&1\end{array}\right] \right)^T=\left[\begin{array}{cc}0&1\\-3&5\end{array}\right]^T=\left[\begin{array}{cc}0&-3\\1&5\end{array}\right]$

$(B)^T=\right]\left[\begin{array}{cc}-1&1\\0&1\end{array}\right] ^T=\right]\left[\begin{array}{cc}-1&0\\1&1\end{array}\right]\\\\(A)^T=\left[\begin{array}{cc}0&1\\3&2\end{array}\right]^T=\right]\left[\begin{array}{cc}0&3\\1&2\end{array}\right]\\(B)^T(A)^T=\right]\left[\begin{array}{cc}0&-3\\1&5\end{array}\right]$

Explicação passo a passo: