# Linear Algebra: Finding the Standard Matrix from a Function

## Homework Statement

Find the standard matrix of T(f(t)) = f(3t-2) from P2 to P2.

n/a

## The Attempt at a Solution

The overall question has to do with finding the determinants, so the matrix is provided; however, I want to know how the author came up with the standard matrix of T.

Any help is greatly appreciated.

vela
Staff Emeritus
Homework Helper
You can find the columns of the matrix representation by applying the transformation to the basis vectors. If you're using the basis {1, t, t2}, the first column of the matrix would correspond to T(1), the second column to T(t), and the third column to T(t2).

Thanks for the guidance. What happens when the basis is Rn? I realize R2 is a 3x3 matrix, R3 is a 4x4, and so on.

vela
Staff Emeritus
Homework Helper
Your question doesn't make sense. Rn is a vector space, not a basis.

Sorry, I was looking at my homework when I typed the last post. I meant vector space.

vela
Staff Emeritus
Homework Helper
Same thing. You choose a basis and apply the transformations to the basis vectors to get the columns of the matrix representing the transformation.

Same thing. You choose a basis and apply the transformations to the basis vectors to get the columns of the matrix representing the transformation.

So, I could choose a basis of 1, t, t2; 1, t, t2, t3; and so on (to tnth)?

vela
Staff Emeritus