Find the matrix X satisfying the matrix equation: X [(5, 3), (-1, -2)]=[(14, 7), (7, 7)]

Question

Find the matrix X satisfying the matrix equation:

\(X\begin{bmatrix}5&3\\-1&-2\end{bmatrix}\)\(=\begin{bmatrix}14&7\\7&7\end{bmatrix}.\)

Answer 1

Let A = \(\begin{bmatrix}5&3\\-1&-2\end{bmatrix}\)B = \(\begin{bmatrix}14&7\\7&7\end{bmatrix}\)

So, AX = B

Or, X = A^–1B

|A| = – 7

Cofactors of A are

C₁₁ = – 2 C₁₂ = 1

C₂₁ = – 3 C₂₂ = 5