Canonical base of polynomial (Linear Algebra)

458 Views Asked by At

I am learning Linear Algebra for few months in school, and I not understand how polynomials works in Linear spaces. Sorry if my nomenclature is different from english one, because I am translating it from Czech.

I have two basis defined as so:

B = (x^2, x, 1)
C = (x^2 + 3x − 2, x − 2, 1)

I know how to convert these to matrices but I don't know if its right

C will be:

| 1  0  0|
| 3  1  0|
|-2 -2  1|

B will be:

| 1  0  0|
| 0  1  0|
| 0  0  1|

Is this right? Or I must compute with polynomials different way