How to prove $W$ is a vector subspace of $V$?
116823
VERIFYING: Proving an $n \times n$ Matrix Vector Space
133087
Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
19946
Let $W$ be a given subspace of $V$ find the orthogonal complement $W^{\perp}$
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v
145462
On the canonical isomorphism between $V$ and $V^{**}$
95513
Proving $W$ is a subspace of $P_{2}$
91022
How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
4319
Vector space can be written as direct sum of subspaces
83449
Proof with 3D vectors
123665
A question in Subspaces in linear algebra
146143
Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
131609
Prove that $Au\cdot v = u\cdot A^Tv$
124786
Prove that V contains a subspace of each dimension
67191
When is the union of a family of subspaces of a vector space also a subspace?
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
106487
Let $S$ and $W$ be subsets of a vector space $V$. Show that if $S$ is a subset of $W$, then $\mathrm{span}(S)$ is a subspace of $\mathrm{span}(W)$