7

Part of 1995 IMC

Problems(1)

IMC 1995 Problem 7

Source: IMC 1995

A

3\times 3

real matrix such that the vectors

Au

u

are orthogonal for every column vector

u\in \mathbb{R}^{3}

. Prove that: a)

A^{T}=-A

. b) there exists a vector

v \in \mathbb{R}^{3}

Au=v\times u

u\in \mathbb{R}^{3}

v \times u

denotes the vector product in

\mathbb{R}^{3}

linear algebramatrixvector