Solve the matrix equation [(5, 4), (1, 1)]X = [(1, -2), (1, 3)] where X is a 2x2 matrix.

Question

Solve the matrix equation \(\begin{bmatrix}5&4\\1&1\end{bmatrix}X\)\(=\begin{bmatrix}1&-2\\1&3\end{bmatrix}\), where X is a 2x2 matrix.

Answer 1

Let A =  \(\begin{bmatrix}5&4\\1&1\end{bmatrix}\)\(B=\begin{bmatrix}1&-2\\1&3\end{bmatrix}\) 

So, AX = B

Or, X = A^–1B

|A| = 1

Cofactors of A are:

C₁₁ = 1 C₁₂ = – 1

C₂₁ = – 4 C₂₂ = 5