Question

If \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] then find matrix \( A \).

Hint:

To solve matrix equations of the form \( MA = B \), multiply both sides by the inverse of matrix \( M \) to isolate matrix \( A \).

Answer 1

We are given the matrix equation: \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] We need to find the matrix \( A \). To do this, we can multiply both sides of the equation by the inverse of the matrix \( \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} \) (if it is invertible). Let matrix \( M = \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} \). Then: \[ A = M^{-1} \times \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] Find the inverse of \( M \) and multiply it with the given matrix to get the final result.