Purchase Solution

# Orthogonal Matrix : Diagonalizability

Not what you're looking for?

Dtermine whether or not the following matrix
A= 5 0 2
0 5 0
2 0 5
is diagonalizable. If it is, then determine
P'-1(P inverse)AP.

##### Solution Summary

Eigenvlaues, determinants and inverses are used to determine the diagonlizability of a given matrix.

##### Solution Preview

If a matrix is diagonalizable, then the matrix will have n ( or in this case 3) independent eigenvalues:

Set up the equation: det(A-rI) = 0 to get the characteristic equations:

| 5-r 0 2 |
| 0 5-r 0 | = 0
| 2 0 5-r|

(5-r)^3 - 4(5-r) = 0
(5-r)[(5-r)^2 - 4] = 0

Thus ...

##### Free BrainMass Quizzes

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

##### Probability Quiz

Some questions on probability