Question

In Exercises 9-10, find bases for the null space and row space of A. [i -1 37 2 0 -1] 9. (a) A = 5 -4 -4| (b) A = 4 :17 -6 2 Lo O o [ 1 4 5 27 10. (a) A = 2 1 3 0 1-1 3 2 2 i 4 5 3 - 1 (b) A = 1 1 -1 0 -1 1 2 3 5 6 4 -2 97 -1 -1 7 8

Answer 1

-3 det (A) = ! (-8-24) +3(10 +28) + 3-30+28)| - 32 + || 4 -6 l14-32 82 #0. Rowe of A aze Linearly indefendent and hence basis fur the w -'. farm foceofA. So B= m a banis for A. Ramk (A)= 3 > Nullity A= 0 [By mk nulhity theorem *: det A F0 -> Null. space of A is *0. hes Null space no basij 2. Det(A) =0 Linenly ard (2,0, -1) and (4,0,2) ane dependent Herau, ow pace has dimausion 1 ared B={12,0,-1)} is a basis. by remte nullity theorem; nullitg(a= 2

let Null sfrace of A -) l,0,?) and (0,!, Lineanly indefiendent `s" of 0. are few so Hen ce is a basis B: for space of A. sull