Given the matrix A= where i=-1, without finding the eigenvalues ot the matrix which of the following is correct: a) The eigenvalues are both real b) Both eigenvalues are complex with equal imaginary parts with opposite sign.

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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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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2 9:07 O145% “",llO
O O -M- 100 Jo
. Given the matrix A=
where i=-1, without finding the eigenvalues ot
the matrix which of the following is correct:
a) The eigenvalues are both real
b) Both eigenvalues are complex with equal imaginary parts with opposite sign.
c) Both eigenvalues are complex with equal real parts and unequal imaginary pa. ts
d) The eigenvalues are both pure imaginary
e) None of the above
5/9
Transcribed Image Text:2 9:07 O145% “",llO O O -M- 100 Jo . Given the matrix A= where i=-1, without finding the eigenvalues ot the matrix which of the following is correct: a) The eigenvalues are both real b) Both eigenvalues are complex with equal imaginary parts with opposite sign. c) Both eigenvalues are complex with equal real parts and unequal imaginary pa. ts d) The eigenvalues are both pure imaginary e) None of the above 5/9
O O -M- 100 Jo
2. Which sentence is FALSE?
a A 2x2 real matrix has two eigenvalues -1 and1
b. A 2x2 real symmetric matrix has eigenvalues 1 and -1
C A 2x2 real matrix has eigenvalues 1+j and 1-2)
d. A 2x2 real matrix has eigenvalues 3+j5 and 3-js
e None of the above
6/9
Transcribed Image Text:O O -M- 100 Jo 2. Which sentence is FALSE? a A 2x2 real matrix has two eigenvalues -1 and1 b. A 2x2 real symmetric matrix has eigenvalues 1 and -1 C A 2x2 real matrix has eigenvalues 1+j and 1-2) d. A 2x2 real matrix has eigenvalues 3+j5 and 3-js e None of the above 6/9
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