# Thread: Solving the column vector for the usual basis.

1. ## Solving the column vector for the usual basis.

Hi everyone! I've been stuck on this problem for the last hour and i need some sort of hint or help for this.

let
$\displaystyle v=2x^3 - 5x^2 + x - 1 \in R_{3} [x]$. Write the column vector v e-hat for the usual basis, i.e. $\displaystyle 1, x, x^2, x^3$

I've been taught to use the Talyor's series but Im confused about how i can go about with that. Thanks!

2. Originally Posted by Layla
Hi everyone! I've been stuck on this problem for the last hour and i need some sort of hint or help for this.

let
$\displaystyle v=2x^3 - 5x^2 + x - 1 \in R_{3} [x]$. Write the column vector v e-hat for the usual basis, i.e. $\displaystyle 1, x, x^2, x^3$

I've been taught to use the Talyor's series but Im confused about how i can go about with that. Thanks!
Why is this not:

$\displaystyle \left[ {\begin{array}{*{20}c} - 1 \\ + 1 \\ - 5 \\ 2 \\ \end{array}} \right]$

This does not involve Taylor series, you are just required to write a vector in a 3 dimensional real or complex vector space in terms of the given basis.

RonL