Question

(1 point) Suppose that A is a 3 × 3 matrix. For each of the question a A after the given row operation is performed. Then give E-1 d), find the elementary matrix E such that EA gives the matrix resulting from

Answer 1

a) R_2 leftarrow 1/2 R_2 E = [1 0 0 0 1/2 0 0 0 1], E^-1 = [1 0 0 0 2 0 0 0 1] b) R_3 leftarrow -4R_3 E = [1 0 0 0 1 0 0 0 -4], E^-1 = [1 0 0 0 1 0 0 0 -1/4] c) R_1 doubleheadarrow R_3 E = [0 0 1 0 1 0 1 0 0], E^-1 = [0 0 1 0 1 0 1 0 0] d) R_2 leftarrow R_2 + 5R_3 E = [1 0 0 0 1 0 0 5 1], E^-1 = [1 0 0 0 1 0 0 -5 1]