Question

Qual deve ser o valor de x na matriz para que seu determinante seja igual a 5?

$\rm B = \begin{bmatrix} \rm x + 1 &4 \\ \rm x & 3 \end{bmatrix}$

A) -2

B) -1

C) 0

D) 1

E) 2
​

Answer 1

$\Large\displaystyle\text{ \begin{gathered} \boxed{ \boxed{ \bf x = - 2 }} \end{gathered} }$

Portanto:

$\Large\displaystyle\text{ \begin{gathered} \boxed{ \boxed{ \bf{Letra\: A}}}\end{gathered} }$

Explicação passo-a-passo:

$\Large\displaystyle\begin{gathered} \tt det \: B = (x + 1) \cdot3 - 4 \cdot{x} \end{gathered}$

$\Large\displaystyle\begin{gathered} \tt det \: B = 3x + 3 - 4x \end{gathered}$

$\Large\displaystyle\begin{gathered} \tt det \: B = - x + 3 \end{gathered}$

Sabendo que esse determinante é igual a 5, então temos que:

$\Large\displaystyle\begin{gathered} \tt - x + 3 = 5 \end{gathered}$

$\Large\displaystyle\begin{gathered} \tt - x = 5 - 3\end{gathered}$

$\Large\displaystyle\begin{gathered} \tt - x = 2 \: \end{gathered}$

$\Large\displaystyle\begin{gathered} \tt x = \frac{2}{ - 1} \end{gathered}$

$\Large\displaystyle\begin{gathered} \tt x = - 2 \end{gathered}$