Question 10

Explanation

Given matrix $A = \begin{pmatrix} 5 & 3 - x \\ -1 & 1 \end{pmatrix}$ and its determinant is $8$.

The formula for the determinant of a $2 \times 2$ matrix $A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is $\det(A) = ad - bc$.

Let's calculate the determinant of matrix $A$:

Given $\det(A) = 8$, then:

So, the value of $x$ is $0$.