# Linear algebra| finding a base

First of all, sorry if my English or any of the terms that I used are incorrect, I am learning math in a different language than english.

So after not being able to study for the past two months I started going over Linear algebra again and need some help to get back in.

I am stuck on this question: Given the following:

V = R4[x] (that's supposed to be a small 4 on the bottom for 4)

dim U = 3

Looking at the sub-space "U": U={$p(-1)=p^n(-1)=0$}

Find a base for B of U where the coefficient of X in every polynomial at the base is equal to -200

I have tried finding a general expression: ax^4+bx^3+cx^2+dx+eAnd tried using x=-1 and get some kind of expression out of the general one, but I got to nowhere with that.

Now cause of the dimU=3 I know the base needs to be 3 linearly independent vectors and I can guess them but I want to do it the right and full solution using a general expression.

Thank you all!

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

- answered
- 142 views
- $2.00

### Related Questions

- Find eigenvalues and eigenvectors of $\begin{pmatrix} 1 & 6 & 0 \\ 0& 2 & 1 \\ 0 & 1 & 2 \end{pmatrix} $
- Let $H$ be the subset of all 3x3 matrices that satisfy $A^T$ = $-A$. Carefully prove that $H$ is a subspace of $M_{3x3} $ . Then find a basis for $H$.
- (Short deadline) Linear Algebra
- Prove that $V={(𝑥_1,𝑥_2,⋯,𝑥_n) \in ℝ^n ∣ 𝑥_1+𝑥_2+...+𝑥_{𝑛−1}−2𝑥_𝑛=0}\}$ is a subspace of $\R^n$.
- [Linear Algebra] $T$-invariant subspace
- Linear algebra
- Find $x$ so that $\begin{pmatrix} 1 & 0 & c \\ 0 & a & -b \\ -\frac{1}{a} & x & x^2 \end{pmatrix}$ is invertible
- Consider the matrix, calculate a basis of the null space and column space