- #1
Rijad Hadzic
- 321
- 20
Homework Statement
Determine the characteristic polynomials, eigenvalues, and corresponding eigenspaces of the given 2x2 matricies
Homework Equations
The Attempt at a Solution
[itex]
\begin{pmatrix}
5 & 2\\
-8 & -3 \\
\end{pmatrix}
[/itex]
thus
[itex]
\begin{pmatrix}
5-\lambda & 2\\
-8 & -3-\lambda \\
\end{pmatrix}
[/itex]
determinant is = to: [itex] \lambda^2 -2\lambda + 1 [/itex]
which gives value lambda = 1
plugging into [itex]
\begin{pmatrix}
5-\lambda & 2\\
-8 & -3-\lambda \\
\end{pmatrix}
[/itex]
you get[itex]
\begin{pmatrix}
4 & 2\\
-8 & -4 \\
\end{pmatrix}
[/itex]
using rref you get[itex]
\begin{pmatrix}
1 & .5\\
0 & 0\\
\end{pmatrix}
[/itex]
setting x2 = r, I get eigenspace r*[itex]
\begin{pmatrix}
-1/2\\
1 \\
\end{pmatrix}
[/itex]
but my book is telling me the anser is r*[itex]
\begin{pmatrix}
1\\
-2 \\
\end{pmatrix}
[/itex]
our answers are the same thing right?