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# Cramer's Rule, solving system of linear equations

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I must solve the following linear equations using matrix methods.

x+y-z=-8

3x-y+z=-4

-x+2y+2z=21

I am trying to understand the method of solving for variables of linear equation by forming them into a matrix and solving for the variables. Please help.

https://brainmass.com/math/linear-algebra/cramers-rule-solving-system-linear-equations-36708

#### Solution Preview

See the attached file.
There are three methods of solving systems of linear equations using matrices.
1. Row elimination method.
2. Cramer's Rule
3. Inverse matrix method.

Here the question is x+y-z=-8

3x-y+z=-4

-x+2y+2z=21

Now we have to find the value of x, y and z using any one of the matrices method.

Here we are going to use the second method called Cramer's rule.

Step:1

Write the coefficient matrix of the system (call this matrix A); if it is square matrix (square matrix is nothing but equal number of rows and columns) , you may continue, otherwise Cramer's rule is not applicable here.

Here we can continue with cramer's rule because the given matrix is square matrix.

The co efficient matrix of this system is
1 1 -1
...

#### Solution Summary

Solving system of linear equations three variables using Cramer's rule is provided in the solution with step-by-step details.

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