Question

Solve the system of equations using the inverse of the coefficient matrix of the equivalent matrix equation.
-2x- y+5z=-7
-7y+2z=-16
2x+7y+8z=6

Answer 1

it forms the form of Ax = b
where A = coefficient matrix, x is vector \(\left[\begin{matrix}x\\y\\z\end{matrix}\right]\) and b = \(\left[\begin{matrix}-7\\-16\\6\end{matrix}\right]\)
then \(\left[\begin{matrix}x\\y\\z\end{matrix}\right]\) = \(A^-b\)
short calculation will give you \(A^-=\left[\begin{matrix}-35/103&43/206&33/206\\2/103&-13/103&2/103\\7/103&6/103&7/103\end{matrix}\right]\)
so, \(A^-b=\left[\begin{matrix}x\\y\\z\end{matrix}\right]= \left[\begin{matrix}0\\2\\-1\end{matrix}\right]\)
or x =0, y =2 and z = -1