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Chapter 5: Q25E (page 263)

TRUE OR FALSE

25. [3-443] is an orthogonal matrix.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Step-by-step solution Step 1: Determine the definition of an orthogonal matrix

A square matrix with real numbers or elements is said to be an orthogonal matrix if its transpose is equal to its inverse matrix.

Or it can be said that, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

02

Consider an example

For example,

Suppose A is a square matrix with real elements and of n脳norder and AT is the transpose of A. Then according to the definition, if AT=A-1 is satisfied, then,

A路AT=I

Consider the matrix below:

3-443

The column vectors are no unit vectors in this matrix.

Thus, the matrix will not be an orthogonal matrix.

Hence, the given statement is false.

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Most popular questions from this chapter

Using paper and pencil, find the QR factorization of the matrices in Exercises 15 through 28. Compare with Exercises 1 through 14.

15.[21-2]

Question:TRUE OR FALSE?If matrices A and Bare commute, then A must commuteBT withas well.

Consider the vectors

ur=[11...1]andvr=[11...1]inRn

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If the nxnmatrices Aand Bare orthogonal, which of the matrices in Exercise 5 through 11 must be orthogonal as well? B-1AB.
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