Solving Linear Algebra Homework: Help Needed!

[madmax2006]

Homework Statement

http://img136.imageshack.us/img136/8452/linalg.png

Homework Equations

I'm trying to figure out what it's asking me to do, as soon as I figure that out, I maybe be able to figure out the equation...

We've gone over stuff like finding the Vector OQ(->) on something like this..
http://img24.imageshack.us/img24/8452/linalg.png

Anybody have a clue what it's asking?

I've seen equations like;
||a|| = sqrt ( A^TA)

and

http://img689.imageshack.us/img689/8452/linalg.png

and some others.. Thanks

 

[HallsofIvy]

The "column space" of matrix A is the subspace spanned by its columns. One way to find the projection of a vector on a subspace is:

Construct a basis for the subspace.
Add vectors to extend to a basis for the entire space.
Write your given vector in that basis.

Drop the terms involving basis vectors not in the subspace.

In this case, if the columns themselves are independent vectors, you can use the column vectors as your basis for the subspace.