Question

Assume that the matrix A is row equivalent to B. Find a basis for the row space of the matrix A. T 2 - 3 4 1-5 -1 A= -4 0 - 5 3 0-3 8 3 1 - 3 2 - 4 1 3 0 -2 0 0 0 0 -4 0 1 3 3 -5 - 8 -15 21 0 0 0 1-3

Answer 1

Basis for a space is the set which is linearly independent and span the all element of the space.

The given matrin A= 1 3 - 4 017 2 4 -5 3-3 T1-5 0-32) [-3-1 8 3 -4 Let us apply elementary row operation on the matrix A. 3 -4 017 R2-2R, T1.3 -4 0 17 1 2 4 - 53-3 R2 ZR1 I 1-5 10 2 3 3-51 0-32 RB-R, Torg 4-3 IL 1-3 -1 8 3-4 Ry+BR 10 8 -4 3-1) TI 3 - 4 o17 1 3 - 4 017 To -2 3 3-5 10-2 33-5 =B. 0 -8 4-31 R₂-4R2 Loo -8-1521 Loo oool 10 0 0 0 0 Therefore A is row equivalent to B. And we see that! A has three linearly independent row which span the 4 row! of A. Ais Therefore basis for the row space of Rut R, 11393 -15 21 II 1-5