Orthogonal projection onto column space of matrix
Solution 1:
U=span{(1,1,1),(-1,2,1)} Observe that (0,1,0)=(1\3)(1,1,1)+(1/3)(-1,2,-1) Since (0,1,0)belongs to U So orthogonal projection of (0,1,0) on U is (0,1,0). Hence, option 1 is correct.
U=span{(1,1,1),(-1,2,1)} Observe that (0,1,0)=(1\3)(1,1,1)+(1/3)(-1,2,-1) Since (0,1,0)belongs to U So orthogonal projection of (0,1,0) on U is (0,1,0). Hence, option 1 is correct.