Prove that V1 and V2 are subspaces and find a basis for them
70021
Verify if symmetric matrices form a subspace
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
102371
Proving that two vector spaces of equal dimension are isomorphic
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
158156
Finding the dual basis for the space of polynomials of degree $\leq$ 2
15560
Prove that the union of three subspaces of $V$ is a subspace iff one of the subspaces contains the other two.
74623
Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$
100749
How to find bases for a subspace defined by an equation
50159
How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
52888
Find all values of a for which $\{v_1,v_2,v_3\}$ form a basis for ${\bf R}^3$
81879
$Av=λv$ basis proof problems
67191
When is the union of a family of subspaces of a vector space also a subspace?
125212
How to Show that the Only Subspaces of $R^2$ are the zero subspace, $R^2$ itself, and the lines through the origin
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
78604
How to find basis of intersection of 2 vector spaces with given basis?
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$