MATH 2331 Lecture Notes - Gaussian Elimination, Row Echelon Form, 32X

• School: Northeastern University
• Department: Mathematics
• Course: MATH 2331
• Professor: Rita Jimenez Rolland

Document Summary

Find the solution(s) of the system of equations. X1 x2 + 4x5 = 2 x3 x5 x4 x5. In the above example, x2 and x5 are known as free variables. Requirements: leading coe cients in each equation equal to 1, leading variable in each equation doesn"t appear elsewhere, leading variables appear in a natural order . 2x1 + 4x2 2x3 + 2x4 + 4x5 = 2 x1 + 2x2 x3 + x4 + 2x5 = 1 x1 + 2x2 x3 + 2x4. 5x1 + 10x2 4x3 + 5x4 + 9x5 = 1 (-5i) x1 + 2x2 x3 + x4 + 2x5 = 1 (+iii) x4 2x5. = 4 (-iii) x1 + 2x2 x4 + 5x5 = 1 (+ii) x4 2x5. = 6 (-2ii) x1 + 2x2 + 3x5 = 2 x4 2x5. X1 = 2 2x2 3x5 x3 = 4 + x5 x4 = 3 + 2x5.