Coordinates relative to a basis (linear algebra)

[hocuspocus102]

Homework Statement

The set B = {-4-x^2, -8+4x-2x^2, -14+12x-4x^2} is a basis for P2. Find the coordinates of p(x) = (-2 +0x -x^2) relative to this basis.

Homework Equations

n/a

The Attempt at a Solution

so the set would be in a matrix like this:
|-4 0 -1|
|-8 4 -2|
|-14 12 -4| and multiplying this by

|-2|
| 0|
|-1| as the vector for p(x) gives

| 9|
|18|
|32| but that's not the right answer and I thought that's how you'd do it.

 

[Mark44]

Homework Statement

The set B = {-4-x^2, -8+4x-2x^2, -14+12x-4x^2} is a basis for P2. Find the coordinates of p(x) = (-2 +0x -x^2) relative to this basis.

Homework Equations

n/a

The Attempt at a Solution

so the set would be in a matrix like this:
|-4 0 -1|
|-8 4 -2|
|-14 12 -4| and multiplying this by

|-2|
| 0|
|-1| as the vector for p(x) gives

| 9|
|18|
|32| but that's not the right answer and I thought that's how you'd do it.

You're going at this the wrong way around. You want the vector c = <c1, c2, c3>^T such that Ac = <-2, 0, -1>^T, where A is the matrix you have above.

 

[hocuspocus102]

oh ok, so if multiply A inverse times <-2, 0, -1> would it be right? I tried that and got <-5/2, 1, 12> which I checked but is still the wrong answer. Did I just put the coordinates in the wrong order or something? because the inverse thing makes sense but it didn't accept my answer. thanks.

 

[Mark44]

Those aren't the right coordinates. The coordinates I got check.

 

[hocuspocus102]

oh ok, I figured it out, thanks a lot!