Question 7 - Week 6 Practice

Question

Let

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

be the linear transformation determined by

T(1,0)=(\alpha-6,-4)

and

T(0,1)=(3,\alpha+1)

, where

\alpha\in\mathbb{R}

. Let

\alpha_1

and

\alpha_2

be the minimum and maximum values, respectively, of

\alpha

for which

T

fails to be injective. Find

\alpha_2^2-\alpha_1^2

Practice question