View Single Post
PirateFan308
#1
Nov24-11, 08:48 PM
P: 94
1. The problem statement, all variables and given/known data
For the following matrix, find the value of t, if any, so that the following matrix is diagonalizable

[tex]A=
\begin{pmatrix}
5 & -2 & 4\\
0 & 3 & t\\
0 & 0 & 5
\end{pmatrix}
[/tex]


3. The attempt at a solution
In order for A to be diagonalizable, we need 3 linearly independent eigenvectors, that is, 3 linearly independent eigenvalues

[tex]det(A-xI)=det
\begin{pmatrix}
5-x & -2 & 4\\
0 & 3-x & t\\
0 & 0 & 5-x
\end{pmatrix}
[/tex]
[tex]=(5-x)det
\begin{pmatrix}
3-x & t\\
0 & 5-x
\end{pmatrix}
[/tex]
[tex]= (5-x)((3-x)(5-x)-0t)[/tex]

The eigenvalues are 3 and 5.
Obviously, it doesn't matter what t is, we will not be able to get the matrix A to be diagonalizable.

My professor said that he thought there was one correct value for t (but he wasn't sure). Is what I've done correct?
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100