Prove that the union of two subspaces of $V$ is a subspace of $V$ if and only if one of the subspaces of $v$ is contained in the other.
11301
Union of two vector subspaces not a subspace?
62077
Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
119782
Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
15576
Addition of two subspaces
4151
Every subspace of a vector space has a complement
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
43068
Let A and B be sets. Show that A is a subset of B if and only if for any set C, one has A union C is a subset of B union C.
78833
Can a basis for a vector space $V$ can be restricted to a basis for any subspace $W$?
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
114524
Proof Verification: the orthogonal complement of the column space is the left nullspace
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
95513
Proving $W$ is a subspace of $P_{2}$
120641
Intersection of three vector subspaces
146664
The union of two linearly independent subsets
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 $\mathrm{span}(W)$
88185
Proof that a subspace $A$ of a complete metric space $X$ is complete iff $A$ is closed
41347
The dimension of the intersection of two vector subspaces