MATH 2574H Study Guide - Midterm Guide: Coefficient Matrix, Row And Column Vectors, Row Echelon Form
Document Summary
Consistent: system has 1 (no free variables) or more solutions (1+ free variables, more variables than eqns) Homogeneous systems (ax = 0) are always consistent. Inconsistent: system has no solution (matrix contains a row [0 0 0 0 0 b] where b doesn"t equal 0 implies that 0 = b) Gaussian elimination (multiply row by non-zero constant, swap 2 rows, replace row w/ linear combination of itself and other row) echelon form (not unique) Start off with [a|i] and do gauss-jordan elimination [i|a-1] *remember, to be invertible, the matrix must be square and row equivalent to i. Ways to solve a system of equations ax = b. Use gauss-jordan elimination on augmented matrix to get reduced echelon form [a b] Multiply b by inverse of a (x = a-1b) Cramer"s rule: only solves for one of the x components, though.
