A 2x2 matrix has trace -13. One of its eigenvalues is -9. What is the other eigenvalue?
A 2x2 matrix has trace -13. One of its eigenvalues is -9. What is the other eigenvalue?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
A 2x2 matrix has trace -13. One of its eigenvalues is -9. What is the other eigenvalue?
Expert Solution
Step 1
given that matrix A has order 2x2
and trace of A is -13
and also given that one of eigen value of A is -9
we know that from the properties of eigen values of any matrix
the sum of eigen of values of a given matrix = trace of a given matrix .........(1)
let we consider the second eigen value of 2x2 matrix is x
then from equation (1)
-9+x = -13
x = -13+9=-4
x=-4
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