Question

Matrix Methods/Linear Algebra: Please show all work and justify the answer! Just need Part C, the null Space and Part D please.

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

ANSWER

G AX=0 A=li -2 0-6 12 0 0 0 - 6 XI -90 O 01 AX=0 > X2 D. 0 OOD X3 *4) N-202-6%q=0 13 +2144=0 13=-904 10,=QW₂+644 Null(A) quat 6 xq W2 merencan -224 N4 12 0 0 O -2 Thus Basis for Null Al = 1 2 lo 1 @ Dimension of the null space of A is a dim (NUIT (A)) = 2