Question

Given the matrix equation: \[A = \begin{pmatrix} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{pmatrix} \quad A \cdot X = B\]
Where \( A \) is the matrix, \( X \) is the unknown vector, and \( B \) is a constant vector. Solve for \( X \).

Hint:

To solve matrix equations of the form \( A \cdot X = B \), calculate the inverse of \( A \) and multiply both sides by \( A^{-1} \), i.e., \( X = A^{-1} \cdot B \).

Answer 1

The matrix equation \( A \cdot X = B \) can be solved by finding the inverse of \( A \) and multiplying both sides by \( A^{-1} \): \[ X = A^{-1} \cdot B \] To solve this, compute the inverse of matrix \( A \) and then multiply by the vector \( B \).