Question

Page 8 of 9 HW-07 EEL-3120 Problem No. 7.7 10 pts 7 -2 0 -53 A--2 0 -5 7 3 0 -5 7 22 l) find k such that Nul(A) is a subspace of R 2) find k such that Col(A) is a subspace of R Show all your work, do not skip steps Displaying only answer is not enough to get credit. Solution (Show all intermediate steps, fonnulas, calculations, explanations and comments below this line. Don't write above this line

Answer 1

"Given that using row operation in A So, A = [7 -2 0 -2 0 -5 0 -5 7 -5 7 2 3 3 2] R_2 rightarrow TR_2 + 2 R_3 ~ [7 0 0 -2 -4 -5 0 -35 7 -5 -39 2 3 -27 2] R_3 rightarrow TR_2 + 2 R_2 ~ [7 0 0 -2 -4 0 0 -35 203 -5 -39 203 3 27 -127] = A^1 (say) This is row echelon form of A here 3 non zero rounds in A^1 hence rank (A) = 3 "" row space (A) = column space (A)"" Now by rank nullity theorem if T: V rightarrow 0 is LT: R^5 - t_1 rank (T) + Nullity (T) - dim (R^5) Nu