Question 6 - Week 8 Practice

Question

Consider

\mathbb{R}^2

with the usual inner product. Let

T:\mathbb{R}^2\to\mathbb{R}^2

be an orthogonal transformation given by

T(x,y)=(ax+by,\ cx+dy)

for all

x,y\in\mathbb{R}

, and let

A

be the matrix representation of

T

with respect to the standard ordered basis. If

a=1

and

\det(A)<0

, find

b+c+d

Practice question