Orthogonalization math problem

[suspenc3]

Homework Statement

$$\left(\begin{array}{ccc}0&1&0\\1&-2&0\\0&0&3\end{array}\right)$$

Homework Equations

|A-Lambda(I)| etc...

let T = lambda

The Attempt at a Solution

$$\left(\begin{array}{ccc}0&1&0\\1&-2&0\\0&0&3\end{array}\right)$$

$$\left(\begin{array}{ccc}-T&1&0\\1&-2-T&0\\0&0&3-T\end{array}\right)$$

cant I just multiply -T(minor11)+(-1)(1)(minor21)?

The answers in the book are different...can anyon help

 

[Hootenanny]

Could you please state the question as given please. I am guessing that the question wants you to find a set of orthogonal vectors which span R³. Does the question mention orthonormalization?

 

[HallsofIvy]

The "problem statement" is NOT just a matrix! What do you want to DO with the matrix?

You appear to be trying to find the eigenvalues. Yes, you can expand the determinant by the either the first row or the first column- you shouldn't have to ask that.

You say the answers in the back of the book are "different"! Different from what? You have told us neither what answers you got nor what the answers are in the back of the book. Not to mention that you never said what the problem was!