If \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 32\), find the value of x.

If \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix} = 32\), find the value of x.

Answer Details

The determinant of a 2x2 matrix [a, b; c, d] is given by \(ad-bc\). Here we are given the determinant of the matrix \(\begin{vmatrix} 4 & x \\ 5 & 3 \end{vmatrix}\) to be 32. So, we have \((4 \times 3) - (x \times 5) = 32\). Simplifying this equation gives us \(12 - 5x = 32\). Solving for x, we get \(x = -4\). Therefore, the value of x is -4.