Homework SourseFind three distinct eigenvalues The matrix C 3 0 0 9 20 30
Find three distinct eigenvalues
The matrix C = [3 0 0 -9 -20 -30 6 10 15] has three distinct eigenvalues, lambda_1Solution
Characteristic equation is |C-I| = 0
Hence,
det of 3- 0 0
-9 -20- -30 = 0
6 10 15-
(3-) [(-20-) ( 15-) + 300 ] = 0
(3-) = 0 (-20-) ( 15-) + 300 = 0
= 3 -300 + 20 -15 + 2 + 300 = 0
2 + 5 = 0
( + 5 ) = 0
= 0 ,-5
Therefore,
= -5 , 0 , 3
Hence,
1= -5 , 2 = 0, 3 = 3
![Find three distinct eigenvalues The matrix C = [3 0 0 -9 -20 -30 6 10 15] has three distinct eigenvalues, lambda_1 SolutionCharacteristic equation is |C-I| = 0](/WebImages/30/find-three-distinct-eigenvalues-the-matrix-c-3-0-0-9-20-30-1086160-1761571174-0.webp "Find three distinct eigenvalues The matrix C = [3 0 0 -9 -20 -30 6 10 15] has three distinct eigenvalues, lambda_1 SolutionCharacteristic equation is |C-I| = 0")
