Not sure where this goes, Linear Algebra question.

[LinearAlgebra]

I really need help with how to go about doing this question...not sure if this is beyong the scope of this board but I'm in Grade 12 so here goes:

"Consider the linear space of quadratic polynomials. Define a basis for this space and determine the matrix that represents differentiation with respect to your basis."

Thanks ahead for any response.

 

[stapel]

What are the elements in the space of quadratic polynomials? (Hint: Think of your basic quadratic, and the terms you would need in order to build such.)

I'm not sure what is meant by "the matrix" for differentiation (perhaps the coordinate matrix?), but think about the basic rules for differentiating polynomial terms. Then consider what differentiation would do to the elements of your basis. Find the mapping from that.

Eliz.

 

[pka]

The usual basis for the linear space of quadratic polynomials is \(\displaystyle \{ x^2 ,x,1\}\).
The polynomial \(\displaystyle ax^2 + bx + c\) might be represented by the column vector \(\displaystyle \left[ {\matrix{
a \cr
b \cr
c \cr

} } \right]\).

The derivative \(\displaystyle 2ax + b\) can be gotten by the matrix \(\displaystyle \left[ {\matrix{
0 & 0 & 0 \cr
2 & 0 & 0 \cr
0 & 1 & 0 \cr

} } \right]\)