×
Log in to StudySoup
Get Full Access to Thousands of Study Materials at Your School
Join StudySoup for FREE
Get Full Access to Thousands of Study Materials at Your School

Already have an account? Login here
×
Reset your password

Solved: In Exercises 714, use determinants to decide whether the given matrix is

Elementary Linear Algebra: Applications Version | 10th Edition | ISBN: 9780470432051 | Authors: Howard Anton, Chris Rorres ISBN: 9780470432051 396

Solution for problem 13 Chapter 2.3

Elementary Linear Algebra: Applications Version | 10th Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
Elementary Linear Algebra: Applications Version | 10th Edition | ISBN: 9780470432051 | Authors: Howard Anton, Chris Rorres

Elementary Linear Algebra: Applications Version | 10th Edition

4 5 1 271 Reviews
12
0
Problem 13

In Exercises 714, use determinants to decide whether the given matrix is invertible.

Step-by-Step Solution:
Step 1 of 3

Section 4.3 EIGENVALUES OF SPECIAL MATRICES Example: Find the eigenvalues.  A=  1 14λ  AI λ    21 −λ  1−4λ det(A−λ ) = 0 21 −λ () ()−8λ 2 12−+λλ 8 0 λλ−270 −±b − 2 4( )( ) λ = 2a ) 7( ) 1 (24±− − λ = 2 ± =± ==22±4 2 11 22 Theorem: MATRICES WITH REAL NUMBER ENTRIES MAY HAVE COMPLEX EIGENVALUES. Example: Let 12 A =22 Find the eigenvalues. Solution: Set det() − λI = 0 and solve for λ. 2λ AI λ −22 λ  1−2λ −2−2 λ =(1 λλ+=2 ) 4 0 =23+ +λ 42 =λλ 36 3± 9-4(1)(65 1±- λ= = 2 2 53±i = 2 For this class, make sure you know that −= i . This is an "imaginary" number. Complex numbers are in the form a+bi. a is the real part and bi is the imaginary part. Several questions will ask for ___+___i and you’ll have to fill in the blanks. Theorem: FOR A REAL MATRIX, COMPLEX EIGENVALUES OCCUR IN CONJUGATE PAIRS; THAT IS, IF a + bi IS AN EIGENVALUE THEN SO IS a - bi . Example: Which of the following COULD be the eigenvalues for a 33× matrix A. 3,i,− 2 B. −+, 1, i C. −−, 2 +i i 3, 4 D. −−, 2 +ii 3,

Step 2 of 3

Chapter 2.3, Problem 13 is Solved
Step 3 of 3

Textbook: Elementary Linear Algebra: Applications Version
Edition: 10
Author: Howard Anton, Chris Rorres
ISBN: 9780470432051

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Solved: In Exercises 714, use determinants to decide whether the given matrix is