- #1

Mutaja

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## Homework Statement

A polynomial of degree two or less can be written on the form p(x) = a

_{0}+ a

_{1}x + a

_{2}x2.

In standard basis {1, x, x2} the coordinates becomes p(x) = a

_{0}+ a

_{1}x + a

_{2}x2 equivalent to ##[p(x)]_s=\begin{pmatrix}a0\\ a1\\ a2 \end{pmatrix}##.

Part a)

If we replace x with (x-1) in the polynomial, the graph to the polynomial will shift/offset 1 to the right.

Find the transformationmatrix, M, to the transformation

T(p(x)) = p(x-1)

so that

##T=\begin{pmatrix}a0\\ a1\\ a2 \end{pmatrix}## = ##M * \begin{pmatrix}a0\\ a1\\ a2 \end{pmatrix}##

part b)

Find the transformation matrix, Ma, to the transformation

Ta (p(x)) = p(x-a).

## Homework Equations

Transformation matrices, basic rules for dealing with matrices and polynomials. I'm assuming.

## The Attempt at a Solution

I understand polynomials, and I can solve problems where I'm given polynomials and then find transformation matrices or linear dependence/independence. But here I'm lost as to what I'm supposed to do. The a

_{0}, a

_{1}, a

_{2}and (x-1) approach is confusing me.

Any guiding as to what I'm looking for as a starter would be gold here, although I fully understand and respect the forum rules that require me to have at least some work to show. I will continue to try out things and post any progress I make.

I know basic rules of polynomials fairly well, although it's a while since we went through that subject. I also know basic rules for matrices, transformation etc. that I went through with a few people on these forums as well. Also, as I stated above, if I'm given two polynomials and I'm asked to check if they can form a basis or something like that, I'm good to go.

I guess this is somewhat similar to what some people go through when they start basic algebra. Solving numbers - fine. When there's letters involved - that's when the problems start.

Any feedback is appreciated as always, thanks a lot in advance.

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