Finding the dimension of the set of all linear maps mapping $v_1, v_2, v_3$ to zero.
68006
Find the dimensions of some kernel subspaces of $\operatorname{Hom}(V, W)$.
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
85239
Proof $dim(W)=dim(V)=n \implies W=V$
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
34700
Proving that the matrix exponential map is surjective onto the general linear group
77722
Lie algebra of affine linear maps
92510
Proving a vector space is infinite-dimensional
38033
A surjective linear map into a finite dimensional space is open
153747
Sub-dimensional linear subspaces of $\mathbb{R}^{n}$ have measure zero.
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
60731
Factorization of a map between CW complexes
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
60684
Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
37119
Determine Which of the following Sets is a Vector Space
41520
Prove that $L(V,W)$ forms a vector space
140225
Linear transformation maps the first quadrant to a closed set