Question

Matrix Methods/Linear Algebra: Please show all work and justify the answer!

3 -6 9 0 1 -2 0 -6 3. Let A= 2 -4 7 2 The RREF of Aiso 0 1 2 3 -6 6 -6 0 0 0 (a) (6 points) Find a basis for Col A, the column space of A. 0 (b) (2 points) What is rank A? (c) (6 points) Find a basis for Null A, the null space of A.

Answer 1

(a) Column 1 and 3 of RREF of A are linearly independent. So, Column i and 3 1 and 3 o of A is a basis for Col (A) So, a basis for cold is {(): (?) (3) Non Zero now it RREF of A s 2 So rank (A) = 2 -6 24 (e) do 72 2 ) -18 23 o o o 24 2- 202 - 624 H3 +224 = 0 = x3=-224 222 + 6x4 24 6 60-6 ༧-。。 A s Null • 12).(:)} Basis for