Question

Use matrix inversion to solve the collection of systems of linear equations. HINT [See Example 4.] (a) −x − 4y + 2z = −10 x + 2y − z = 11 x + y − z = 14

Answer 1

Answer:

Step-by-step explanation:

given is a system of linear equations in 3 variables as

$-x - 4y + 2z = −10\\ x + 2y - z = 11 \\x + y - z = 14$

This can be represented in matrix form as

AX=B Or

$\left[\begin{array}{ccc}-1&-4&2\\1&2&-1\\1&1&-1\end{array}\right] *\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}-10\\11\\14\end{array}\right]$

So solution set

X would be $A^{-1} B$

|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