# 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
- 221 views
- $2.00

### Related Questions

- 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 $H$.
- Does $\sum_{n=2}^{\infty}\frac{\sin n}{n \ln n}$ converge or diverge?
- Linear Algebra: Quadratic Forms and Matrix Norms
- Linear Algebra - Matrices (Multiple Choice Question) (1st Year College)
- Step by step method to solve the following problem: find coordinates of B.
- For what values k is the system consistent?
- Consider the plane in R^4 , calculate an orthonormal basis
- Singular Value Decomposition Example