Question 14

Explanation

Given $A = \begin{pmatrix} 1 & 2 \\ 1 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & 1 \\ 1 & 3 \end{pmatrix}$ with $AC = B$

Finding Matrix C

From the equation $AC = B$, multiply both sides by $A^{-1}$

However, since the order of matrix multiplication matters

Determining Inverse of Matrix A

For matrix $A = \begin{pmatrix} 1 & 2 \\ 1 & 3 \end{pmatrix}$, its inverse is

Calculating Matrix C

Calculate $C = BA^{-1}$

Calculating Determinant of C

The determinant of matrix $C$ is

Therefore, the determinant of matrix $C$ is $11$