Why does 1 vector $\vec{v_1}$ in $\mathbb{R}^n$ that is linearly independent imply that $\vec{v_1} \neq \vec{0}$?
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
140711
Linear independence of images by $A$ of vectors whose span trivially intersects $\ker(A)$
42334
Does $\lambda$ $\mathbf u$ $= 0$ imply $\lambda = 0$ or $\mathbf u$ $= 0$?
123505
how to prove vector norm equivalence in finite dimensional space($\mathbb{R}^{n}$)?
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
55461
How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
18967
Linear independence of $\sin(x)$ and $\cos(x)$
127488
If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
72567
Does a set of $n$ independent vectors in $R^{n}$ always span $R^{n}$?
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
31069
Smallest and largest values of $\|\vec{v}-\vec{w}\|$
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
37206
$\mathbb{R}^n\times\{0\}$ has measure zero in $\mathbb{R}^{n+1}$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
92600
Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
152147
Why is a set of orthonormal vectors linearly independent?