Question

Given the matrix 1 1 1 1 -1 1 -1 3 1 А -1 (i) Find a basis for the column space of A. (ii) Find an orthonormal basis for the column space of A.

Answer 1

. başiş for col (A) 11 basis for col (A) Let them be X. , X2, x3 Let Orthogonal basis be, v= V Gauss-schmidt process X₂ Vi V = x, 12 = X₂ - V, Т. V₂ V = 3- = x - x *31 Vi JV viv, .. V, - X, A

一的 > V = - 关 % v = 1+1+1+1) |x)= =+ -- (g)、 十 = 04:2 - V2 6 - TIN orthogonal basis of col (A) 3 12-12 Orthonosmal basis 1R 23 3 ? ? 3 25 0 1V 2 2 -2 23 3 ! =x 2 、 3 26

Orthonosmal basis of col (A) 1 2 3 4 2 V 2V3 Mladen -IN IN IN ร่ง3 // to