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Chapter 3: Q25P (page 123)
Verify (6.14) by multiplying the matrices and using trigonometric addition formulas.
The result is verified by using the trigonometric addition formulas.
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Find the symmetric equations and the parametric equations of a line, and/or the equation of the plane satisfying the following given conditions.
Line through and parallel to the line
Note in Section 6 [see (6.15)] that, for the given matrix A, we found , so it was easy to find all the powers of A. It is not usually this easy to find high powers of a matrix directly. Try it for the square matrix Min equation (11.1). Then use the method outlined in Problem 57 to find.
Let each of the following matrices represent an active transformation of vectors in (x,y)plane (axes fixed, vector rotated or reflected).As in Example 3, show that each matrix is orthogonal, find its determinant and find its rotation angle, or find the line of reflection.
Question: Give numerical examples of: a symmetric matrix; a skew-symmetric matrix; a real matrix; a pure imaginary matrix.
Compute the product of each of the matrices in Problem 4with its transpose [see (2.2)or (9.1)in both orders, that isand, etc.
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