Question

Let A=|-39 28|
|-60 43|
has an eigenvalue of lambda = 1.
An eigenvector for lambda = 1
has the form | a |
|-10|
What is the value of a? (If the values in A are too large or unwieldy, you may be able to regenerate a new problem depending on the settings of this assignment.)

Answer 1

let the eigenvector we are finding for be x. now we know that:
Ax=lambda*x
Ax=x
so what we need to do is solve with this matrix:
\[\left[\begin{matrix}-39 & 28 \\ -60 & 43\end{matrix}\right]\left(\begin{matrix}a \\ -10\end{matrix}\right)=\left(\begin{matrix}a \\ -10\end{matrix}\right)\]
now to find a, we see that we only need to solve this simple:
-39a-280=a