Linear algebra - find orthonormal basis for matrix

[Eagerissac]

I'm stumped on the two questions in the following picture below. I've been solving problems that involve me converting a given basis for W into an orthogonal basis by using the Gram-Schmidt Process. I'm just confused as to what I'm supposed to do here because it just gives me a giant variable U whereas for most questions I'm supposed to find U1, U2, U3, etc to form the orthogonal basis. I know what an orthonormal basis is as well but I'm just confused by what I'm supposed to do with U.

I'm also not sure what b) means by if U is a 4 by 4 matrix but I think it will make more sense once I get how to do a). I would appreciate any help


This is a part of some lecture notes I've been using to help me solve similar problems. Like here, I'm trying to find U1, U2, and U3, but in the question above it just gives me U and I don't know what to do with it.

 

[Steven G]

b) I suspect hat you are not being clear. You said I'm also not sure what b) means by if U is a 4 by 4 matrix. I am sure that you know what a 4x4 matrix is. So what exactly are you confused about?

 

[HallsofIvy]

What concerns me is that you are give "y" and "U" and then are asked for the orthogonal projection of y on W, apparently without knowing what "W" is!