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Chapter 3: Q21P (page 112)
In Problem 21 to 23, find the angle between the given planes.
and
The angle between the given points is .
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In Problemsto show that the given functions are linearly independent.
Show that a real Hermitian matrix is symmetric. Show that a real unitary matrix is orthogonal. Note: Thus, we see that Hermitian is the complex analogue of symmetric, and unitary is the complex analogue of orthogonal. (See Section 11.)
Find the Eigen values and Eigen vectors of the following matrices. Do some problems by hand to be sure you understand what the process means. Then check your results by computer.
Question: For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint:Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using
6.
Show that the given lines intersect and find the acute angle between them.
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