MATH102 Study Guide - Midterm Guide: 1 Bc, Identity Matrix, Row Echelon Form

• School: University of Alberta
• Department: Mathematics
• Course: MATH102
• Professor: Ian Blokland

Document Summary

If a matrix is row reduced to reduced row-echelon form by two different sequences of elementary row operations, the resulting matrices might be different. If a is a matrix with rank 4, then the homogeneous system ax = 0 requires 4 parameters. Rank tells you the number of variables that don"t need to become parameters. (cid:3) (cid:3) If a and b are n n matrices such that ab = 0, then either a = 0 or b = 0. It is not too dif cult to come up with an example (size 2 2, say) of nonzero (cid:3) matrices a and b so that ab evaluates to the zero matrix. It is always true that a+ b = b+ a for every m n matrices a and b. If a is an invertible square matrix, then (a 1) Every square matrix can be expressed as a product of elementary matrices.