Prove that if $x^TAx = 0 \Rightarrow Ax = 0$
118949
If $(Tx \mathbin{|} x) = 0$ for all $x$ then $T = 0$
30860
Prove that $f(x)=0$ in $[-1,1]$.
66451
In a ring, how do we prove that a * 0 = 0?
96327
Show that $a^x+b^x+c^x>(a+b+c)^x$ for all $a,b,c>0$ and $0<x<1$
5410
Prove that $a^2 + b^2 \geq 8$ if $ x^4 + ax^3 + 2x^2 + bx + 1 = 0 $ has at least one real root.
105852
How to verify whether or not there exists a vector $x$ such that $Ax > 0$?
156235
Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms?
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
142725
The general solution of $x^a = a^x$ for real $a >0$
32155
Prove that if for every $x \in \mathbb{R}^N$ $Ax=Bx$ then $A=B$
129564
Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
115583
prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
158335
Why is this $0 = 1$ proof wrong?