MathDB

Problem 10

Part of 2019 LIMIT Category C

Problems(2)

inscribing cylinder in sphere to maximize volume

Source: LIMIT 2019 CCS1 P10

4/28/2021
A right circular cylinder is inscribed in a sphere of radius 3\sqrt3. What is the height of the cylinder when its volume is maximal?
geometry3D geometrysphere
maximize even entries in A if det(A)=1 (3x3)

Source: LIMIT 2019 CCS2 P10

4/28/2021
Let A∈M3(Z)A\in M_3(\mathbb Z) such that det⁡(A)=1\det(A)=1. What is the maximum possible number of entries of AA that are even?
Matricesmatrixlinear algebra