Mathematics

Problem

The coefficient matrix of a system of three equations in variables

u,\,v,\,w

A = \begin{pmatrix}1 & -2 & 3\\ 0 & 4 & 5\\ 2 & 1 & -1\end{pmatrix}

. If the inverse of

A

is given by

A^{-1} = \begin{pmatrix}1 & 0 & 1\\ -\tfrac14 & \tfrac14 & \tfrac54\\ \tfrac32 & -\tfrac12 & -\tfrac32\end{pmatrix}

and the constant matrix is

B = \begin{pmatrix}2\\-1\\3\end{pmatrix}

, determine the column vector

X = \begin{pmatrix}u\\v\\w\end{pmatrix}