MAT223H1 Study Guide - Midterm Guide: Augmented Matrix, Distributive Property, Row Echelon Form
Document Summary
February 25, 2010: bland, s. kudla, r. sadykov, s. uppal. Consider the system of linear equations x1 + 2x2 + x3 4x4 + x5 = 1 x1 + 2x2 x3 + 2x4 + x5 = 5. 2x1 + 4x2 + x3 5x4 = 2 x1 + 2x2 + 3x3 10x4 + x5 = 3. Find all solutions and express your answer in parametric form. We form the augmented matrix and reduce to row echelon form. Since we have three leading ones in columns one, three and four, x2, x5 can be any real numbers. Set x5 = t, x2 = s. then the third row gives. 3x4 2x5 = 0 so x4 = t, 3 second row means that x3 3x4 = 2 so x3 = 3x4 2 = 2t 2 and from the rst row x1+2x2+x3 4x4+x5 = 1 so x1 = 2x2 x3+4x4 x5+1 = 2s 2t+2+ Thus t + 3 x1 = 2s 1.
