In this question, you will apply the Gram-Schmidt process.

In this question, you will apply the Gram-Schmidt process.

The subspace V has a basis of three vectors u1=⎛⎝⎜⎜(1,3,0,0)⎞⎠⎟⎟, u2=⎛⎝⎜⎜(4,2,10,0)⎞⎠⎟⎟ and u3=(⎛⎝⎜⎜5,35,-9,1)

⎞⎠⎟⎟a) Normalize vector u1 to give the vector v1. b) Find the component of u2 orthogonal to v1.Enter the answer exactly. This will become the vector v′2.

c) Normalize v′2,to give the vector v2.Enter the answer exactly.

d) Find the component of u3orthogonal to both v1and v2.Enter the answer exactly. This will become the vector v′3.

e) Normalize v′3,to give the vector v3.Enter the answer exactly, possibly with a square-root. For example, the square root of 5 is entered as sqrt(5)

f) Project the vector (⎛⎝⎜⎜-5,15,-41,11)⎞⎠⎟⎟ onto the subspace spanned by {v1,v2,v3}

g) Project the vector ⎛⎝⎜⎜(-8,6,-8,2)⎞⎠⎟⎟ onto the same subspace.