University eigenvalues and eigenvectors quiz to download as PDF

This University eigenvalues and eigenvectors quiz has 10 short questions for pupils aged 18-19. Type your answer, check it straight away and read the explanation when you get one wrong.

University eigenvalues and eigenvectors quiz: the 10 questions

Eigenvalues of \(\begin{pmatrix}2&0\\0&7\end{pmatrix}\)?
Trace of \(\begin{pmatrix}1&2\\3&4\end{pmatrix}\)?
Product of the eigenvalues equals which quantity?
Eigenvalues of \(I_3\)?
If \(\lambda\) is an eigenvalue of \(A\), eigenvalue of \(A^{-1}\)?
Is the zero vector an eigenvector?
Characteristic equation of a \(2\times2\) matrix: \(\lambda^2-(\ ?\ )\lambda+\det A\).
Eigenvalue of \(\begin{pmatrix}1&1\\1&1\end{pmatrix}\) with eigenvector \((1,1)\)?
Number of eigenvalues (with multiplicity) of a \(4\times4\) complex matrix?
Real symmetric matrices have what kind of eigenvalues?

How to use this University eigenvalues and eigenvectors quiz

First, answer every question without a calculator unless the question says so. Then check your answer and read the short explanation. If you get fewer than 7 right, revise the eigenvalues and eigenvectors lesson and try again later. After that, try the multiple choice questions or the eigenvalues and eigenvectors worksheet.

Finally, take this quiz again before a test, because quick retrieval helps you remember. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday.