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Chapter 3: Q8P (page 141)
(a) Prove that. Hint: See.
(b) Verify (9.11), that is, show that (9.10) applies to a product of any number of matrices. Hint: Use (9.10)and (9.8).
a) It is proven that .
b) It is proven that .
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In Problems 8 to 15,use to show that the given functions are linearly independent.
15.
Let each of the following represent an active transformation of the 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 reflectionthe
As in Problem 1, write out in detail in terms of equations like (2.6) for two equations in four unknowns; for four equations in two unknowns.
Find the Eigen values and eigenvectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.
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
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