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Mutaja
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Homework Statement
A polynomial of degree two or less can be written on the form p(x) = a0 + a1x + a2x2.
In standard basis {1, x, x2} the coordinates becomes p(x) = a0 + a1x + a2x2 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 a0, a1, a2 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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