MAT223H1 Study Guide - Midterm Guide: Row Echelon Form, Augmented Matrix, Solution Set
Document Summary
February 14, 2014: garcia-raboso, c. kent, f. murnaghan, k. tyros, s. uppal. 1 of 8: suppose that the given matrix is the augmented matrix of a system of linear equations in the variables x1, x2, x3, x4, x5. 1 1 2 3 4 1. [4] (a) find the reduced echelon form of the given system. Solution: the free variables can be read o the reduced row echelon form as the non-pivot variables. Therefore, the free variables are x3 and x5. [4] (c) find the set of solutions to the given system. Solution: let x3 = t, x5 = s. From the third row: x4 2x5 = 0. From the second row: x2 + x3 x5 = 0. X2 = s t x1 x2 x3 x4 x5. From the rst row: x1 3x3 + 3x5 = 1. X1 = 1 + 3t 3s. Solution: we"ll use the gauss-jordan method to transform (a|i) (i|a 1).
