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Chapter 8: Q34E (page 393)

For which angle(s) 胃can you find four distinct unit vectors in 鈩�3such that the angle between any two of them is胃? Draw a sketch.

Short Answer

Expert verified

The angle between any two of them is胃=109.47掳

Step by step solution

01

Symmetric matrix:

In linear algebra, a symmetric matrix is a square matrix that stays unchanged when its transpose is calculated. That instance, a symmetric matrix is one whose transpose equals the matrix itself.

02

To find θ:

To find胃we must take the inverse of the cosine and as we have n dimensions we take the inverse of the cosine of-1nas represented below:

role="math" localid="1659611016541" 胃=cos-1-1n

The angle胃for which you find four distinct unit vectors insuch that the angle between any two of them isgiven by:

胃=cos-1-13胃=109.47掳

03

Find Four distinct unit vectors in ℝ3:

Four distinct unit vectors in 鈩�3such that the angle between any two of them is胃=109.47掳is represented in the figure:

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Most popular questions from this chapter

For which values of the constants p and q is the matrix

B=[pqLqqpLqMM0MqqLp]

positive definite? (B has p鈥檚 on the diagonal and q鈥檚 elsewhere.) Hint: Exercise 8.1.17 is helpful.

ForA=[211111121111112], find a nonzero vectorv鈫� in鈩�3such thatAv鈫�is orthogonal tov鈫�.

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61.qis indefinite and det A < 0

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where A is a symmetricnxnmatrix. Letv鈬赌 be a unit eigenvector of A, with associated eigenvalue 位. Find q(v鈬赌).

Show that the diagonal elements of a positive definite matrix A are positive.
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