Question

Calcule x de modo que as matrizes A= $\left[\begin{array}{ccc}2&-3\\1&4\end{array}\right]$ e B= $\left[\begin{array}{ccc}4&x\\0&4\end{array}\right]$ sejam comutativas. R: x=0

Answer 1

$Ola'~~~~\mathbb{JIMINE} \\ \\ Para~que~seja~comutativa~deve~ser~que: \\ \\ \boxed{A.B=B.A} \\ \\ \begin{bmatrix}2&-3 \\ 1&4\end{bmatrix}.\begin{bmatrix}4&x \\ 0&4\end{bmatrix}=\begin{bmatrix}4&x \\ 0&4\end{bmatrix}.\begin{bmatrix}2&-3 \\ 1&4\end{bmatrix} \\ \\ \\ \begin{bmatrix}8+0&2x-12 \\ 4+0&x+16\end{bmatrix}=\begin{bmatrix}8+x&-12+4x \\ 0+4&0+16\end{bmatrix} \\ \\ \\ \begin{bmatrix}8&2x-12 \\ 4&x+16\end{bmatrix}=\begin{bmatrix}8+x&-12+4x \\ 4&16\end{bmatrix}$

$Vamos~observar~igualando~cada~uma~delas~para~calcular~o~valor \\ de~''x'' \\ \\ 8=8+x=\ \textgreater \ \boxed{x=0} \\ \\ 2x-12=-12+4x=\ \textgreater \ \boxed{x=0} \\ \\ x+16=16=\ \textgreater \ \boxed{x=0} \\ \\ Por~tando~o~valor~de~\boxed{\boxed{x=0}}~--\ \textgreater \ resposta \\ \\ \\ \mathbb{iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$