Question 6.1.8: Show that λ = 0 is an eigenvalue for the matrix A =[3 -1 5...
Show that λ = 0 is an eigenvalue for the matrix
A=\left[\begin{array}{rrr}3 & -1 & 5 \\2 & 1 & 0 \\4 & 1 & 2\end{array}\right]
From the Big Theorem, Version 8, λ = 0 is an eigenvalue of A if and only if det(A) = 0. By the Shortcut Method, we have
det(A) = (6 + 0 + 10) − (20 − 4 + 0) = 0
so λ = 0 is an eigenvalue of A.
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