Exercise · ZW-EIGENVALUE-AND-EIGENVECTOR-001 · ★☆☆ Basic
Let \(A=\begin{pmatrix}4&1\\2&3\end{pmatrix}\). Which of these numbers is an eigenvalue of \(A\)?
Choose one option.
Show answer
- C. \(5\)
Explanation
Since \(A(1,1)=(5,5)=5(1,1)\), the number 5 is an eigenvalue. The eigenvalues of \(A\) are 2 and 5, so 1, 3 and 4 are not.
Review the concept: Eigenvalue and eigenvector
An eigenvector \(v\) of a square matrix \(A\) is a nonzero vector that \(A\) only stretches, shrinks or flips, without taking it off its line; the factor \(\lambda\) is its eigenvalue.
\[Av=\lambda v,\quad v\neq 0\]
More practice problems: eigenvalue and eigenvector
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