MCV4U1 Matrices and Gaussian Elimination Matrix: A rectangular array (Rows x Columns) of real numbers. Examples: (3 x 3 Matrix) (3 x 2 Matrix) (2 x 2 Matrix) (Zero Matrix) Equal Sign Augmented Matrix: Each Row of an augmented matrix corresponds to one equation. Ex.) Row 2 is equivalent to: x + y + 2z = 9 Each number represents the coefficient of a variable.

Gaussian Elimination Gaussian Elimination is an efficient method for solving systems of equations that uses MATRICES to organize the solution. Augmented Matrix (Row Reduction) Gaussian Elimination Gauss-Jordan Elimination (Row Reduction) Row-Echelon Form Reduced Row-Echelon Form Row Reduction: The process of row reduction uses the following ROW OPERATIONS, to solve systems of equations. 1.) Switch any 2 rows within the matrix. 2.) Multiply/Divide an entire row by a constant. 3.) ADD/SUBTRACT two rows to create replace a row.

Ex.) Use Gaussian Elimination to solve the following systems of equations. a) x + 2y + z = -4 x + 4y + 5z = -18 4x - z = -4 b) 3y - 2z = 19 x - y + 4z = -13 x + 3z = - 6 c) 2x + 3y - z = 13 x - 2y + 3z + 2 = 0 4x + y + 3z = 9 d) x + 2y + 7z - 3 = 0 x - y + z - 4 = 0 3x + 3y + 15z - 10 = 0

Homework:Worksheet - parts (a - f)

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