Linear Algebra: Let U, V be non-zero subspaces of R3, and let W = U ∪ V be the set of vectors which lie in either U or V (or both).
11301
Union of two vector subspaces not a subspace?
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
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
95513
Proving $W$ is a subspace of $P_{2}$
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
113261
How to find a vector space V and decompositions $V=A\oplus B = C\oplus D$ with $A$ isomorphic to $C$ but $B$ is not isomorphic to $D?$
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
102458
Subspace generated by permutations of a vector in a vector space
7462
If X and Y are two sets of vectors in a vector space V, and if X $\subset$ Y, then is span X $\subset$ span Y?
52973
The identity $(u\times v)\cdot(x\times y)=\begin{vmatrix}u\cdot x&v\cdot x\\ u\cdot y&v\cdot y\\\end{vmatrix}$
76160
Dimension of the sum of two vector subspaces
104578
Suppose that $V$ is a vector space, and $W$ is a subspace of $V$. If $V$ is finite dimensional, then prove $W$ too must be finite dimensional.
14429
dimension of a subspace spanned by two subspaces
4374
Geometric interpretation of a vector space and subspace?
67191
When is the union of a family of subspaces of a vector space also a subspace?
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.