These University eigenvalues and eigenvectors multiple choice questions check your understanding of eigenvalues and eigenvectors with 10 questions for pupils aged 18-19. Each question has four answers, and the right one is explained as soon as you choose.
University eigenvalues and eigenvectors multiple choice questions: the 10 questions
\(\mathbf v\neq0\) is an eigenvector if
The eigenvalues of \(\begin{pmatrix}3&0\\0&5\end{pmatrix}\) are
For a \(2\times2\) matrix the eigenvalues sum to
If \(A\) has eigenvalue 3, then \(A^2\) has eigenvalue
A matrix is invertible iff
\(n\) distinct eigenvalues imply
Eigenvalues of \(\begin{pmatrix}0&-1\\1&0\end{pmatrix}\)
If \(A=PDP^{-1}\) then \(A^3=\)
The eigenvalues of an upper triangular matrix are
Cayley-Hamilton: a matrix
How to use these University eigenvalues and eigenvectors multiple choice questions
First, read each question carefully before you look at the four answers. Then work the answer out on paper, so that you do not simply guess. After that, read the explanation, even when you are right. If you score less than 7 out of 10, go back to the eigenvalues and eigenvectors lesson.
Finally, practise more with the eigenvalues and eigenvectors worksheet and the quiz. 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.
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