Prove W is a subspace of V.
86325
Is an increasing union of subspaces a subspace?
134065
A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
76188
Show $(W_1 + W_2 )^\perp = W_1^\perp \cap W_2^\perp$ and $W_1^\perp + W_2^\perp ⊆ (W_1 \cap W_2 )^\perp$
78833
Can a basis for a vector space $V$ can be restricted to a basis for any subspace $W$?
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
135814
Prove certain subsets of $\mathbb R^n$ are subspaces
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
70475
Proving a basis for inner product space V when $||e_j-v_j||< \frac{1}{\sqrt{n}}$.
83449
Proof with 3D vectors
95513
Proving $W$ is a subspace of $P_{2}$
4319
Vector space can be written as direct sum of subspaces
45337
Suppose that $V, W$ are closed in $X$ and that $V\cap W, V\cup W$ are connected. Show that $V$ and $W$ are connected.
147590
If $L$ is regular, prove that $\sqrt{L}=\left\{ w : ww\in L\right\}$ is regular
6547
Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$
13899
Proof that $-v = (-1)*v$