Question

Find the bases for Col A and Nul A. and then state the dimension of these subspaces for the matrix A and an echelon form of A below. 1 3 8 -1 -3 1 3 8 -1 -3 2 7 200 -4 0 1 4 2 -3 - 12 - 36 2 13000 3 13 40 0 -11 000 Abasis for Col A is given by (Use a comma to separate vectors as needed.)

Answer 1

ī o Given A1 38 2 7 20 0-4 -3 -12 -36 2 13 1 3 1 400 - - col A = span column of A - Span $117 131987 12 /71 1201 11-12 -36 odo = Span 1 / 2 Since 20-47 0 10/= Il linearly independial 7 4 sima 13

- 30 basis of cola = 8 тоо Null space of A - Şa =0 ГІ 3 8 - 1 -3 1/2 2 1 20 o -4 15 -3 -12 -34 2 3 || 3 3 13 ч. 2 -{} в 1 - 2 2 - o o o 1, 2 1) ) » +32 + 8- -3ҡr =0 , +242 =0 24 + 2 - - + = - 2 x- x, -4 - 24 - 2%- - 4х + 4-2х = -47, + 2х- ч = 2х2 + 8 +24 13 ч- 2 - 3 (4* - 2xr) - 87, - 2 +3 x - 412 - сх. – & – 2 + 3 = +*– 5* -

Je, we get, 1 = - 2 0% 3 -51 22 2-413 +214 - -24 So Nuall A - 7 | 1973 - S15) 21:13 14 € #2 .7XA [.61) San / ๐ - - - so, basis of ul A is if 147 do- col A = 3 How dimension of p 4 Nu F -2 coln dimension of Bow echelon form of A is 3 Nula of a 4 A 152