Math Help - Linear Algebra.Similar to a triangle matrix.pls help!

1. Linear Algebra.Similar to a triangle matrix.pls help!

We have the following matrix :

$A=\begin{pmatrix} 2 &0&0 \\ 0&0&1 \\ 0&-1&0 \end{pmatrix}$

How can I found a triangle matrix similar to the initial matrix.

I was pleased if someone show me the step by step solution because I have 2 more matrices to do exactly the same procedure.

2. Here's my idea: Find the eigenvalues of the matrix A and put them into a diagonal matrix.

Since a diagonal matrix is both upper and lower triangular, it's triangular.

Is there anything wrong with this idea?

3. Originally Posted by Showcase_22
Here's my idea: Find the eigenvalues of the matrix A and put them into a diagonal matrix.

Since a diagonal matrix is both upper and lower triangular, it's triangular.

Is there anything wrong with this idea?
This is right (diagonal matrix is both upper and lower triangular) but I think that the exercise asks to find exactly a triangular matrix which mean something less than you refer(diagonal). Anyway thanks alot for replying my post.

4. Originally Posted by ypatia
We have the following matrix :

$A=\begin{pmatrix} 2 &0&0 \\ 0&0&1 \\ 0&-1&0 \end{pmatrix}$

How can I found a triangle matrix similar to the initial matrix.

I was pleased if someone show me the step by step solution because I have 2 more matrices to do exactly the same procedure.