▲ 4 r/LinearAlgebra
column space basis question
For this (b) part i, I used the method of transposing A, row-reducing Aᵀ, and taking the non-zero rows of RREF(Aᵀ) as the basis vectors. is it correct or not? and for part ii
Part (i) — bases NOT necessarily from A:
Row space basis → take non-zero rows of RREF(A): { (1, 0, −1), (0, 1, 0) }
Column space basis → transpose A, row-reduce Aᵀ, take non-zero rows: { (1, 0, −5, −3), (0, 1, 2, 1) }
Part (ii) — bases that ARE rows/columns of A:
Row space basis → take the pivot rows (rows 1 & 2) from the original A: { (1, 2, −1), (1, 9, −1) }
Column space basis → RREF says cols 1 & 2 are pivots → take those columns from original A: { (1, 1, −3, −2), (2, 9, 8, 3) }
this is the answer basically but my teacher marked it wrong so kindly let me know
u/Kind-Ant-8221 — 11 days ago