Question

Dada as matrizes: A= $\left[\begin{array}{ccc}1&0&2\\0&-1&3\\4&-1&2\end{array}\right]$ B= $\left[\begin{array}{ccc}2&-1&1\\0&3&0\\4&2&1\end{array}\right]$ e C= $\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right]$ Calcule:

a) A.B-B.C
b) (A+B-C).B            R= a) $\left[\begin{array}{ccc}8&4&2\\12&0&3\\12&-5&5\end{array}\right]$      b) $\left[\begin{array}{ccc}16&1&5\\12&9&3\\24&-1&10\end{array}\right]$

Answer 1

$Ola' \\ \\ a)~A.B=B.C \\ \\ \begin{bmatrix}1&0&2 \\ 0&-1&3 \\ 4&-1&2\end{bmatrix} .\begin{bmatrix}2&-1&1 \\ 0&3&0 \\ 4&2&1\end{bmatrix}-\begin{bmatrix}2&-1&1 \\ 0&3&0 \\ 4&2&1\end{bmatrix}.\begin{bmatrix}1&0&0 \\ 0&1&0 \\ 0&0&1\end{bmatrix} \\ \\ \\ ~~~~~~~~~~\begin{bmatrix}10&3&3 \\ 12&3&3 \\ 16&-3&6\end{bmatrix}-\begin{bmatrix}2&-1&1 \\ 0&3&0 \\ 4&2&1\end{bmatrix} \\ \\ \\\boxed{ AB-B.C=\begin{bmatrix}8&4&2 \\ 12&0&3 \\ 12&-5&5\end{bmatrix}}$

$\mathbb{ttttttttttttttttttttttttttttttttttttttt} \\ b)~~(A+B-C).B \\ \\ \Bigg(\begin{bmatrix}1&0&2 \\ 0&-1&3 \\ 4&-1&2\end{bmatrix}+\begin{bmatrix}2&-1&1 \\ 0&3&0 \\ 4&2&1\end{bmatrix}-\begin{bmatrix}1&0&0 \\ 0&1&0 \\ 0&0&1\end{bmatrix}}\Bigg).\begin{bmatrix}2&-1&1 \\ 0&3&0 \\ 4&2&1\end{bmatrix} \\ \\ \\ ~~~~~~~~~~~~~~~~~~~~~~~~\begin{bmatrix}2&-1&3 \\ 0&1&3 \\ 8&1&2\end{bmatrix}.\begin{bmatrix}2&-1&1 \\ 0&3&0 \\ 4&2&1\end{bmatrix}$

$~~~~~~~~~~~~~~~~~~~~ \begin{bmatrix}4+0+12&-2-3+6&2+0+3 \\ 0+0+12&0+3+6&0+0+3 \\ 16+0+8&-8+3+4&8+0+2\end{bmatrix} \\ \\ \\ \boxed{(A+B-C).B=\begin{bmatrix}16&1&5 \\ 12&9&3 \\ 24&-1&10\end{bmatrix}}\\ \\ \\ \mathbb{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx} \\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$