Characteristic polynomials
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In this exercise find the following:(the characteristic polynomial of A, and the eigenvalues of A, and a basis for each eigenspace of A, the algebraic and geometric multiplicity of each eigenvalue.
1) [1 -9
1 -5]
2) [1 1 0
1 0 1
0 1 1 ]
3) [ 1 1 -1
0 2 0
-1 1 1]
4) [ 1 0 3
2 -2 2
3 0 1]
5) [ 3 1 0 0
-1 1 0 0
0 0 1 4
0 0 1 1]
6) [ 1 0 0 0
0 1 0 0
1 1 3 0
-2 1 2 -1]
7) [ 1 1 1 0
4 1 0 1
0 0 -1 1
0 0 2 0].
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Solution Summary
The characteristic polynomial of A, and the eigenvalues of A, and a basis for each eigenspace of A, the algebraic and geometric multiplicity of each eigenvalue are determined.
Education
- BSc, University of Bucharest
- MSc, Ovidius
- MSc, Stony Brook
- PhD (IP), Stony Brook
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