9 Factorial question: number of trailing zeroes in 125! 7 Proofs of AM-GM inequality 5 Prove that a doubly stochastic matrix is a square matrix 4 Null space of $T$ is {$(x,y,z,w)\in R^4:x+y+z+w=0$}. Rank of $(T-4I_4)$ is 3. Then minimal polynomial of $T$ is $x(x-4)$. 3 Sum of binomial and uniform variable? Convolution?

### Reputation (2,366)

 +10 Prove that if a vector space $V$ has a basis of $n$ vectors, then every basis of $V$ must consist of exactly $n$ vectors? +20 Finding integer solutions to a multivariable equation +10 Can these conditions sufficiently solve an equation involving absolute values +10 optimizing the distance between two matrices

### Questions (96)

 4 Probability of having a disease and testing positive for it 3 Cramer Rao lower bound in Cauchy distribution 3 Intersection of all non normal.subgroups of a group 3 Dimension of a range space of a linear operator 2 Finding integer solutions to a multivariable equation

### Tags (151)

 21 linear-algebra × 38 9 real-analysis × 14 15 matrices × 28 9 elementary-number-theory × 2 11 abstract-algebra × 20 9 divisibility 10 group-theory × 21 9 factorial 9 probability × 32 9 contest-math

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 0 Proof of construction of a matrix