Answer:
Step-by-step explanation:
given is a system of linear equations in 3 variables as
[tex]-x - 4y + 2z = −10\\ x + 2y - z = 11 \\x + y - z = 14[/tex]
This can be represented in matrix form as
AX=B Or
[tex]\left[\begin{array}{ccc}-1&-4&2\\1&2&-1\\1&1&-1\end{array}\right] *\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-10\\11\\14\end{array}\right][/tex]
So solution set
X would be [tex]A^{-1} B[/tex]
|A|=-1(-1)+4(0)+2(-1)=--1
Cofactors of A are
-1 0 -1
-2 -1 -3
0 1 2
So inverse of A is
1 2 0
0 1 -1
1 3 -2
Solution set would be
x=12
y=-3
z=-5
