Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

let $V=\mathbb{R}^4$ and let $W=\langle\begin{bmatrix}1&1&0&0\end{bmatrix}^t,\begin{bmatrix}1&0&1&0\end{bmatrix}^t\rangle$. we need to find the subspaces $U$ & $T$ such that $ V=W\bigoplus U$ & $V=W \bigoplus T$ but $U\ne T$.

share|improve this question
4  
What have you tried ? –  Belgi Oct 13 '12 at 6:10
    
For example, can you find one space $U$ such that $V=W\oplus U$? –  Gerry Myerson Oct 13 '12 at 11:34
add comment

1 Answer 1

HINT: Look at a simpler problem first. Let $X=\{\langle x,0\rangle:x\in\Bbb R\}$, a subspace of $\Bbb R^2$. Can you find subspaces $V$ and $W$ of $\Bbb R^2$ such that $\Bbb R^2=X\oplus V=X\oplus W$, but $V\ne W$?

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.