Schaum's Outline of Linear Algebra by Seymour Lipschutz

Author:Seymour Lipschutz
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2018-11-08T05:00:00+00:00

Method 2. Find P-1 by row reducing M = [P, I] to the form [I, P-1:

Thus,

6.15. Suppose the x-axis and y-axis in the plane R 2 are rotated counterclockwise 45° so that the new x0-axis and y0-axis are along the line y = x and the line y = x, respectively.

(a) Find the change-of-basis matrix P.

(b) Find the coordinates of the point A (5, 6) under the given rotation.

(a) The unit vectors in the direction of the new x0- and y0-axes are

(The unit vectors in the direction of the original x and y axes are the usual basis of R2.) Thus, write the coordinates of u1 and u2 as columns to obtain

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