Solving Systems by Gaussian Elimination (Linear Algebra)
Free printable university Linear Algebra worksheet on solving 3x3 linear systems by Gaussian elimination, row reducing the augmented matrix to RREF, with exact integer solutions and full working.
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Linear Algebra · Math worksheet
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Linear Algebra: Solving Systems by Gaussian Elimination
Solve each system by writing its augmented matrix and row reducing to reduced row echelon form (RREF). Every system has a unique integer solution. Matrices are written in row form, e.g. [1, 2; 3, 4].
- 1.Solve by Gaussian elimination: 4x - 3y - 2z = 12; -x - y - 4z = -14; 2x + 2y - 4z = -20
- 2.Solve by Gaussian elimination: 3x - 2y - 2z = 1; 2x + 2y + 2z = 4; -x - y - 2z = -5
- 3.Solve by Gaussian elimination: -2x + 4y + z = 4; 2x + 2y - 4z = 26; -x + 4y + 2z = 7
- 4.Solve by Gaussian elimination: -3x + y - 3z = 16; -4x + 2y - 2z = 20; -x - 3y - 4z = 5
- 5.Solve by Gaussian elimination: -3x - y + z = -13; -x - 2y - 2z = 6; -3x - 4y - 3z = 5
- 6.Solve by Gaussian elimination: -x + 4y - 2z = 4; 4x + 3y + 3z = -7; -x - y + z = 5
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