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Systems of Three Equations

Problems

Solving using Matrices and Row Reduction

Solving using Matrices and Cramer's Rule

Problem : Solve the following system using matrices and row reduction:

2x - y + 3z = - 15
x + 2y - z = 15
2x - 3y - 3z = 7

(x, y, z) = (2, 4, - 5)

Problem : Solve the following system using matrices and row reduction:

2x + 2y - 5z = - 9
5x - 2y + z = 4
7x + 4y - 4z = 3

(x, y, z) = (1, 2, 3)

Problem : Solve the following system using matrices and row reduction:

2x + y + z = - 11
-3x - y + 2z = - 1
x + 2y - z = 2

(x, y, z) = (- 3, 0, - 5)

Problem : Solve the following system using matrices and row reduction:

5x + y + z = 5
2x + 2y + 2z = - 6
3x - y + 4z = - 9

(x, y, z) = (2, - 1, - 4)

Problem : Solve the following system using matrices and row reduction:

x - 2y - z = 0
2x + y - 3z = 7
-3x - y + 4z = - 11

(x, y, z) = (7, 2, 3)

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