Proof : $S$ a subspace of a vector space is generated by $n$ vectors, any $m$ vectors in $S$ , where $m > n$ are linearly dependent.
40409
If a subspace S is spanned by $n$ vectors, any subset of S with $m>n$ vectors is linearly dependent
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
4151
Every subspace of a vector space has a complement
51397
If a field $F$ is such that $\left|F\right|>n-1$ why is $V$ a vector space over $F$ not equal to the union of $n$ proper subspaces of $V$
120766
Prove ${y_n}$ is a basis for a Hilbert space $H$.
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
92510
Proving a vector space is infinite-dimensional
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
19396
For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
150135
The intersection of an infinite number of subspaces is a subspace
53261
Show that Pn is an (n+1)-dimensional subspace
131132
Proofs using vector properties
139951
Direct Sum of vector subspaces
43282
Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
70413
A vector space over $R$ is not a countable union of proper subspaces
23372
Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set