Answered: A = a %3|

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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For what value(s) of a does the matrix have the characteristics below?
(a) A has an eigenvalue of multiplicity 2.
(b) A has −1 and 2 as eigenvalues.
(c) A has real eigenvalues.

Expert Solution

Introduction:

Consider the matrix,

It's characteristic equation is given by,

Part a)

The matrix A has eigenvalue with multiplicity 2.

For this to happen, convert equation (1) into complete square form.

Consider equation (1),

Take square roots on both sides.

For repeated eigenvalues, square root term must be zero.

It is possible only when,

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