Question

Dadas as matrizes abaixo, determine os valores de x, y e z na seguinte igualdade:

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao~de~igualdade~de~matrizes}\\\sf Duas~matrizes~s\tilde ao~iguais~se~e~somente~se\\\sf forem~do~mesmo~tipo\\\sf e~os~elementos~de~mesma~posic_{\!\!,}\tiilde ao~forem~iguais\end{array}}$

$\Large\boxed{\begin{array}{l}\rm Dadas~as~matrizes~abaixo,determine\\\rm os~valores~de~x,t~e~z~na~seguinte\\\rm igualdade:\\\begin{bmatrix}\sf x+15&\sf4z-32&\sf3y^3\end{bmatrix}=\begin{bmatrix}\sf-35&\sf-112&\sf-15\sqrt[\sf2]{\sf9}\end{bmatrix}\end{array}}$

$\large\boxed{\begin{array}{l}\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf Pela~d~\!\!efinic_{\!\!,}\tilde ao~de~igualdade~de~matrizes~temos:\\\sf x+15=-35\\\sf x=-35-15\\\sf x=-50\\\sf 4z-32=-112\\\sf 4z=32-112\\\sf 4z=-80\\\sf z=-\dfrac{80}{4}\\\sf z=-20\\\sf 3y^3=-15\sqrt[\sf2]{\sf9}\\\sf \diagdown\!\!\!\!3y^3=-15\cdot\diagdown\!\!\!\!3\\\sf y^3=-15\\\sf y=\sqrt[\sf3]{\sf-15}\end{array}}$