1

Part of 2005 IMC

Problems(2)

IMC 2005 day 1 pb 1

Source: peter

A

n\times n

matrix such that

A_{ij} = i+j

. Find the rank of

A

. [hide="Remark"]Not asked in the contest:

A

is diagonalisable since real symetric matrix it is not difficult to find its eigenvalues.

linear algebramatrixIMCcollege contests

IMC 2005 day 2 pb1

Source: Peter

f(x)=x^2+bx+c

, M = {x | |f(x)|<1}. Prove

|M|\leq 2\sqrt{2}

(|...| = length of interval(s))

conicsparabolaparameterizationIMCcollege contests