Prove that $a$ or $v$ = 0
13880
Example of vector space such that $cv = 0$ where $c \ne 0$ and $v \ne \vec{0}$
151806
Prove that $A^k = 0 $ iff $A^2 = 0$
61472
If $0<x<y$, then prove that $\sqrt{x} <\sqrt{y}$ and $x <\sqrt{xy} <y$
57981
Alternative proof of $a\times0= 0$
34693
Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
150885
$v \otimes v' = v' \otimes v$ implies $v = av'$
113892
Show $A \in \cal F$ exists, such that $\mathbb P(A)=1$ and $\mathbb Q(A)=0$.
76790
Condition to guarantee $f=0$ on $[a,b]$
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
149907
$T\circ T=0:V\rightarrow V \implies R(T) \subset N(T)$
142725
The general solution of $x^a = a^x$ for real $a >0$
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
140988
Prove $\exp(x)\exp(y)=\exp(y)\exp(x)$ if $[x,y]=0$.
54737
Proof that $V = \sum_k U_k$ and $\dim V=\sum_k \dim U_k$ implies $V=\oplus_k U_k$
146339
Proof of -(-v)=v in a vector space
2959
Prove $0! = 1$ from first principles
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$