Question

Please help. fan/medal
What is the solution of the matrix equation?

Answer 1

Hint: You are given a matrix equation of the form
\(Ax = B\) where \(A = \begin{bmatrix} 5 & -2 \\ 2 & -1\end{bmatrix}\), \(B = \begin{bmatrix} 2 \\ -4\end{bmatrix}\) and \(x\) is the solution matrix.

To isolate x, you multiply both sides by \(A^{-1}\) to get:
\(x = A^{-1}B\)

In other words, to find the solution matrix, find \(A^{-1}\) then multiply it by \(B\).

Just as a reminder:
\(A^{-1} = \dfrac{1}{|A|}\begin{bmatrix} d & -b \\-c & a\end{bmatrix}\)