Help please Apply The GramSchmidt method to The matrix B 1

Help please

Apply The Gram-Schmidt method to The matrix B = [1 0 1 0 3 3 1 -1 2 4 0 2] to find an orthogonal basis for the column space of B.

Solution

Given that B =

Do elementary column operations to bring to a reduced column echelon form

C2-C1 = C2,

C2= C3-C2

C3=C3-4C2

C3/-10

C2 =C2-3C3

= C

Now C is the orthogonal basis for B

1	3	2
0	3	4
1	1	0
0	-1	2