Problem 20

Explanation

We are given matrix $A$ as follows:

It is known that the determinant of matrix $A$ is $4$. The determinant formula for a $2 \times 2$ matrix like $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is $ad - bc$.

Calculating the Determinant

We will calculate the determinant of matrix $A$ and set it equal to $4$:

So, the value of $x$ is $2$.