Question

step by step please

Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee that the matrix is diagonalizable. (Recall that the matrix may be diagonalizable even though it is not guaranteed to be diagonalizable by the theorem shown below.) Sufficient Condition for Diagonalization If an n x matrix A has n distinct eigenvalues, then the corresponding cigenvectors are linearly independent and A is diagonalizable 02 Find the eigenvalues. (Enter your answers as a comma-separated list.) 2 =

Answer 1

1st

An Upper Triangular Matrix have its Eigen Values are its Diagonal Elements

So eigen values are - 1 , - 4 , 2

All are distinct , so Matrix is Diagonalizable

2nd

Det. of Matrix = 0 , So atleast One Eigen Value is 0

Trace of Matrix = Sum of Daigonal Elements = Sum of Eigen Value = 9 + 9 = 18

So other Eigen Value is 18

Since Eigen Value are Distinct

So Matrix is Diagonalizable