Question

linear algebra

Find N(A) A = 1 -3 4 -1 9 -2 6 -6 -1 -10 -39 -6 -6 -3 3-94 9 0 a. 6 N(A) = 4 -1 ୨ 10 E. N(A) = 0 3 2 ) 0 0 C T ୨ NA - -6 -1 -10. -] ୨ =5 - -] ୨ ) d, N(A) = 3 0 0 2 0 5 1 1 0 0 0 NA - 1 1 0 0 -2 0 f. 2 NIA) = 0 1 0 2

part a

part b

Answer 1

oo A= 0 0 - - 0 443 4 2 2 17 2. 2. नक्ष्य ना 2 O Prod 1 - 10 NOW ATA x= ATb. and the augmented matrin for this system, 14 ly 2 2 2. 10 2 o 2 I Ri 4 - Now we ato ro w reduced the matrix 2 2 O 1 - 5 IR 1 0 O - 5) R2R - Rg 2 1 R: R3-R, 08:10 R/2 R₂ k (4136

Then the system reduced to, 2 x + x3 My My 33 then up-5-t, m=24t. Then the least square solution is, let- 0 04 5-6 -3+t -2-K t ng 5t - t tee 1 option b 1-3 A- TT -2 9 -10 -3 -3 9 -6 -6 -9 4 9 o 3 row reducing we aget, A i-3 5 6 0 O O B 0 O 0 0 0 0 o Now we will sobre x=(x 2 ng ay na) giver, to find the null space BY:0, Where x - 342 +509-0, 2-3x4=0, x5 20. take, Xat, xyas, Then xy = 3.8-5t, azt, nys, Xs=0 3 There for, 3 5 35-st t 1 tt 3t mhoo up D

3 in Null space of A,N(A)= -- 10 0 1 w 2 0