# Diagonal matrix

Not what you're looking for?

For the problem, refer to the linear transformation T: R^3→R^3 given by T(x) = T(x, y, z) = (2x + 2z, x - y + z, 2x + 2z).

The matrix A = [T]_E is similar to a diagonal matrix D = [T]_F. Write the diagonal matrix D, and demonstrate that it is indeed similar to A by producing the appropriate non-singular matrix and its inverse.

##### Purchase this Solution

##### Solution Summary

This shows how to write diagonal matrix D, and demonstrate that it is similar to another matrix.

##### Solution Preview

T(x, y, z) = (2x + 2z, x - y + z, 2x + 2z)

T(1, 0, 0)= (2, 1, 2)

T(0, 1, 0)= (0, -1, 0)

T(0, 0, 1)= (2, 1, 2)

Then the matrix is:

[2 0 2]

A= [1 -1 1]

...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Solving quadratic inequalities

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

##### Exponential Expressions

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

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

##### Graphs and Functions

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

##### Know Your Linear Equations

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.