AI Tutor
Back to Matrix transformations

Exercise 8

Avg difficulty 2.5

Suppose that T:R2→R2T:\real^2\to\real^2 is a matrix transformation and that T([11])=[3−2],T([−11])=[12]T\left(\twovec{1}{1}\right) = \twovec{3}{-2}, \qquad T\left(\twovec{-1}{1}\right) = \twovec{1}{2}.

  1. Find the vector T([10])T\left(\twovec{1}{0}\right).

  2. Find the matrix AA that defines TT.

  3. Find the vector T([4−5])T\left(\twovec{4}{-5}\right).

Austin, Understanding Linear Algebra, §2.5 Matrix transformations, Exercise 8

AI Tutor

Adapted from Understanding Linear Algebra © 2023 David Austin. Licensed under CC BY 4.0. Source: Understanding Linear Algebra. Imported at revision 3e6dced.