Question

个 please proke S(A) S lease Show me ense Show me your step ond logic, thonks lot !!

please let it be easy to understand, really thank you!

CS is column space, if you need more explanation please tell me.

Answer 1

Given that P = A(A^T A)^-1 A^T = A(A)^-1 (A^T)^-1 A^T = (AA^-1) (A^T)^-1 (A^T) = I_n times I_n = I_n P = I_n (identify matrix of order n) Therefore P is invertible and rank (p) = n. Again Since AA^-1 = I_n, So that A is invertible and Rank (A) = n Now P = I_n and Rank (P) = n i.e the column space of P is only [0 0...0]_n times Zero vector Similarly the column space of a is only [0 0...0]_n times n Therefore C S(P) = C S (A)