Couple Linear Algebra questions?

Question

Where 'P' is a matrix and 'x' is a vector:

Px = the projection of x onto <1,1>. What is the the matrix P relative to the basis { <1, -1>, <1,1>}

I'm thought the answer was:

| 0 1 |
| 0 1 |

Because the projection of <1, -1> onto <1,1> is <0,0> and the projection of <1, 1> onto <1,1> is <1,1>, but my choices are

| 2 1 |
| 1 2 | - A

| 1/2 1/2 |
| 1/2 1/2 | - B

| 0 0 |
| 0 1 | - C

and

| 1 0 |
| 0 0 | - D

---

| a d |
| b c | is the matrix for T relative to the standard basis. What is the matrix for T relative to the basis {<0, -1>, <1, 0>}

I'm completely stumped on this one. Even if someone could just nudge me in the right direction i would be appreciative... Thanks!

Answer 1

For the second one, why don't you figure out:

A. The matrix for the basis {<-1,0>,<0,-1>}
B. The matrix for the basis {<1,0>,<0,-1>}
C. The matrix for the basis {<0.1>,<1,0>}

If you can do B and C you surely can do the actual problem. And A is the same idea as B, only easier. ;)