Question

Put the following matrices into reduced row echelon form and state which columns are pivot columns: (a) -7 A= 3 -7 -2 -3 5 6 -4 0 1 5 2 (b) A= 1 2 1 2 4 3 6 2

Answer 1

SAM a) we have mately 3 -1 -2 A = 5 6 4 O 5 2 Apply elementary www-operations, we get -43 -7/3 - 23 -2 - R₂1 R₂ + R, R37. R₂-2R, 2 6 10 4 16 R, I RI -1/3 -773 -2/3 72 R₂ + ₂ +5 R2 R₂7 R2 2 - 0 - 0 0 6 -2 1 6 12 0 R, TR, + 7 R2 Rz>-1. R3 ½ 2 - O 0 0 1 1 0 0 3 4 R, TR, 2 R3 R21 R₂ - - R3 0 - 0 0 0 - -6 reduced row-echeon youm of A. 0 3 0 0 0 4 FIA) O O T 0-6 Hence, columns I, I and IT are pivot commne

b) we have matly 1 2 A - 2 4 6 3 2 tant apply how - operations, - - R21 R2-2R, R₂ + R3-3R 0 0 -1 0 0 - 2 0 w 0 0 - RAR, + R₂ R₂ + R₃-R2 B₂ 1-1.R₂ 0 0 The reduced row echelon form of A: 12 O 0 0 weflak 0 0 1 q and I Hence, columns I have a kivot element de collemme I and are pivot columne