Science:Math Exam Resources/Courses/MATH152/April 2013/Question A 26

MATH152 April 2013

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Question A 26
Find the eigenvalues of the matrix A where $A={\begin{bmatrix}0&1\\1&0\end{bmatrix}}$

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
Eigenvalues are the roots of the characteristic polynomial given by $\det(A-\lambda I)$.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. Proceeding as in the hint, we have $\det(A-I\lambda )=\det \left({\begin{bmatrix}0&1\\1&0\end{bmatrix}}-{\begin{bmatrix}\lambda &0\\0&\lambda \end{bmatrix}}\right)=\det \left({\begin{bmatrix}-\lambda &1\\1&-\lambda \end{bmatrix}}\right)=\lambda ^{2}-1=(\lambda -1)(\lambda +1)$ and so the eigenvalues are given by $\lambda =\pm 1$

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