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Spring 2009 Math 22 Exam 3 Review Sheet
The exam will be in class on Monday, April 27.
You will not be allowed use of a
calculator or any other device other than your pencil or pen and some scratch paper.
Notes are also not allowed.
In kindness to your fellow testtakers, please turn off all cell
phones and anything else that might beep or be a distraction.
Important topics:
•
Computing eigenvalues and eigenvectors of a 2x2 or 3x3 matrix
•
Basic theory of eigenvalues and eigenvectors
•
Application of eigenvalues and eigenvectors to matrix powers
•
Definition of similar matrices, and what properties similar matrices share
•
Diagonalization, conditions for when a matrix is diagonalizable
•
Kernel and range of a linear transformation
•
Injective and surjective linear transformations
If you have problems with certain topics or want more practice, feel free to stop by my office.
Review problems
1.
Determine the eigenvalues and eigenvectors of the matrix
1
3
4
2
and find an
invertible matrix
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 Spring '08
 Serra

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