Page 527 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Figure 6.6.2
Moreover, since extends 1 unit up the positive -axis,

Thus the transition matrix from to B is

and the transition matrix from B to is

(verify). Thus the new coordinates of a point Q can be computed from its old coordinates by

Exercise Set 6.6

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1.
(a) Show that the matrix

is orthogonal in three ways: by calculating , by using part (b) of Theorem 6.6.1, and by
using part (c) of Theorem 6.6.1.

(b) Find the inverse of the matrix A in part (a).