Question

Assume that the matrix A is row equivalent to B. Without calculations, list rank A and dim Nul A. Then find bases for Col A, Row A, and Nul A. 1 2-2 4-5 1 2-2 -4 -5 00 1 -4 0 0 0 05 3 6 -814-12 -3 -6 14 20 0 rank A 3 dim Nul A= 2 2 812 A basis for Col A is 2 -314 (Use a comma to separate vectors as needed.) 2 A basis for Row Ais-2 4 4 (Use a comma to separate vectors as needed.) A basis for Nul A is (Use a comma to separate vectors as needed.)

Answer 1

B = [1 + 2 - 2 - 4 - 5 0 0 1 1 - 4 0 0 0 0 - 5 0 0 0 0 0] Rightarrow [1 2 - 2 - 4 - 5 0 0 1 1 - 4 0 0 0 0 1 0 0 0 0 0] (R_3 = -R_3/5) Rightarrow [1 2 - 2 - 4 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0] (R_1 = R_1 + 5R_3 R_2 = R_2 + 4R_3) Rightarrow [1 2 0 - 2 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0] (R_1 = R_1 + 2R_2) Rightarrow x_1 + 2x_2 - 2x_4 = 0 x_3 + x_4 = 0 x_5 = 0 Rightarrow x_1 = -2 x_2 + 2x_4 x_3 = -x_4 x_5 = 0 \r\n [x_1 x_2 x_3 x_4 x_5] = [- 2x_2 + 2x_4 x - x_4 x_4 0] = x_2[-2 1 0 0 0] + x_4 [2 0 - 1 1 0] Rightarrow basis for Nul (A) = [[-2 1 0 0 0] , [2 0 - 1 1 0]]