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Chapter 7: Q38E (page 383)

If a 2 x 2matrix R represents a reflection about a line L, then R must be diagonalizable.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Diagonalizable matrix

If any triangular matrix of order n has n distinct eigenvalues, then matrix A is diagonalizable.

02

Explanation for the statement:

A reflection matrix A about a line L has two eigenvalues, first one being 位 1 = 1, with E1 = L , and the other one being 位 2 = -1, with E-1 = L鈯� Since we have two distinct eigenvalues on a 2 x 2 matrix, this means that A is diagonalizable.

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Most popular questions from this chapter

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[010001100]

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