Determine whether S is a subspace of V, if yes find a basis and its dimension.
48113
Find a basis for the vector space of symmetric matrices with an order of $n \times n$
18913
How to find a basis for the intersection of two vector spaces in $\mathbb{R}^n$?
107000
Dimension of intersection of distinct subspaces
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 $D?$
41347
The dimension of the intersection of two vector subspaces
68006
Find the dimensions of some kernel subspaces of $\operatorname{Hom}(V, W)$.
33642
Finite dimensional subspace of $C([0,1])$
60684
Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
88728
Dimensions of vector subspaces in a direct sum are additive
100749
How to find bases for a subspace defined by an equation
40409
If a subspace S is spanned by $n$ vectors, any subset of S with $m>n$ vectors is linearly dependent
45485
Dimension of a subset
124786
Prove that V contains a subspace of each dimension
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
23740
Confused about the definition of subspace