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# Mathematics - Linear Operators explained in this solution

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1. solve the following equations and show work.

2. You are given the following system of linear equations:

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.

e. Calculate the following for

a. A * B
b. -4A
c. AT

4. Solve the following linear system using Gaussian elimination.
Show work.

3x + y - z = -5

-4x + y = 6

6x - 2y + 3z = 2

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

x + 2y - 3z = -22

2x - 6y + 8z = 74

-x - 2y + 4z = 29

##### Solution Summary

Solutions to the posted problems given with step by step explanation and detailed working so that the students could easily understand and use these solutions as model solutions to solve other similar problems. Problems using Gaussian elimination and Cramers rule are also solved in the attached solution file.

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