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# Matrices

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(1.) x-y+2z=13
2x+xy-z=-6
-x+3y + z =-7

a. Provide a coefficient matrix corresponding to the system of linear equations.

b. What is the inverse of this matrix?

c. What is the transpose of this matrix?

d. Find the determinant for this matrix.

(2) A = [2 -3] [-4 1]
[7 4] and B=[ 6 5]
Calculate the following for:
a. A*B
b. -4A
c. A T

3. Solve the following linear system using Gaussian elimination.
Show work.
3x + y-z =.5
-4x + y =6
6x = 2y + 3z =2

4. Solve the following linear system for x using Cramer's rule.
Show work.

x + 2y-z = -22
2x - 6y + 8z = 74
-x -2y + 4z = 29

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https://brainmass.com/math/linear-algebra/matrices-172861

#### Solution Summary

This provides several examples of working with matrices: Gaussian elimination, Cramer's rule, matrix operations, coefficient matrix, inverse, transpose, and determinant.

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