Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
36314
If $Ax = Bx$ for all $x \in C^{n}$, then $A = B$.
154327
$A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
46780
Proving $((a\bmod n) (b\bmod n))\bmod n = ab\bmod n $
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
122213
Proving that if $\langle Ax,x\rangle =0$ for every $x$, then $A$ is the zero operator
15491
Prove that $f:\mathbb R^n\to\mathbb R$ is affine if and only if it is convex and concave
158695
Prove that if $AB$ is invertible then $B$ is invertible.
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
13026
Prove that if AB=I_m, then rk(A)=rk(B).
124562
$f:\mathbb{R}^n \to \mathbb{R}$ has expansion $\sum_i g_i(x)x^i$
54430
For $a,b$ coprime, there exists positive integers $x,y$ such that $ax-by=1$
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] $
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
56818
Prove that if $A$ is positive, then $\exists\;\alpha>0$ such that $\langle Ax, x \rangle\geq \alpha|x|^2$ for $x\in\Bbb{R}^n$
76049
Prove that if $a|b$ and $a|c$ then $a|(sb+tc)$ for all $s, t \in \mathbb{Z}$
27248
If $A$ is an $m \times n$ matrix, prove that $Ax=0$ has infinite solutions $\iff$ $\text{rank}(A)<n$