Practice Practice Problems (33.13) - Diagonalization - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Diagonalize the matrix A = [6 -2; 2 2].
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Calculate the eigenvalues first.
Question 2.
Find the eigenvalues of the matrix A = [1 1; 0 1].
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Use the characteristic polynomial.
3Question 3.
What is the form of a diagonalized matrix?
- PDP-1
- DP-P1
- PDP^-1
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Remember the relationship between the matrices.
4Question 4.
True or False: All symmetric matrices are diagonalizable.
- True
- False
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Consider the properties of symmetric matrices.
Question 5.
Given a matrix A = [3 1; 0 3], prove its non-diagonalizability.
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Examine the eigenspace to conclude.
Question 6.
A symmetric matrix B = [2 1; 1 2] is given, find its eigenvalues and eigenvectors analytically.
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Use the characteristic polynomial to derive eigenvalues.

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