answer true if the statementis always true and false otherwise. In the case ofa true statement, explain or prove your answer. In thecase of a false statement, give an example to show thatthe statement is not always true. If L1 rotates each vector x in R2 by 60◦ and then reflects the resulting vector about the x-axis, and if L2 is a transformation that does the same two operations, but in the reverse order, then L1 = L2.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section: Chapter Questions
Problem 2RQ
Question

answer true if the statement
is always true and false otherwise. In the case of
a true statement, explain or prove your answer. In the
case of a false statement, give an example to show that
the statement is not always true. If L1 rotates each vector x in R2 by 60◦ and then
reflects the resulting vector about the x-axis, and if
L2 is a transformation that does the same two operations,
but in the reverse order, then L1 = L2.

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