1.TheGram-Schmidt process is used to find an orthogonal basis that spans a givensubset of Rn from an original spanning set:

Given a basis {x1, …, xp}for a subspace W ofRn,define

v1 = x1

v2 = x2– projv2(x2)

v3 = x3– projv1(x3)– projv2(x3)

…

vp = xp– projv1(xp) - projv2(xp)- … - projvp-1(xp)

where projv(x) is the projection operator (inprod(u,v)/inprod(u,u))*u and inprodis the inner product.

Then {v1, …, vp} is anorthogonal basis for W and span{x1, …, xp}= span{v1, …, vp}.

Write a SAS prgoram to find an orthogonal basis for Wusing IML.Transform it into anorthonormal basis.

1 2 6

-1 0 2

W = 1 4 3

0 1 0

1 2 0