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Zadania:
1.
Nájdite vlastné hodnoty, vlastné vektory a Jordanov normálny tvar matice
| A) |
 | -5 | -3 | -3 |  | | 4 | 3 | 5 | | 2 | 1 | -1 |
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, | B) |
| 3 | 4 | 4 | | | 1 | 4 | 1 | | -1 | -5 | -2 |
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, | C) |
| 3 | -4 | -4 | | | -4 | 3 | 4 | | 4 | -4 | -5 |
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2.
Nájdite vlastné hodnoty a Jordanov normálny tvar matice
| A) |
| 0 | 3 | 2 | -2 | | | -1 | -3 | -1 | 1 | | 2 | 2 | -1 | 1 | | 0 | -1 | -1 | 0 |
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, | B) |
| 4 | 7 | 6 | 0 | | | -5 | -7 | -5 | 0 | | 4 | 3 | 2 | 0 | | -1 | -2 | -1 | -2 |
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Riešenia:
1.
| A) |
| -2 | 1 | 0 | | | 0 | -2 | 0 | | 0 | 0 | 1 |
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λ=-2: (2,1,1),
λ=1: (1,1,1). | B) |
| 3 | 1 | 0 | | | 0 | 3 | 0 | | 0 | 0 | -1 |
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λ=3: (1,1,1),
λ=-1: (0,1,1). | C) |
| -1 | 0 | 0 | | | 0 | -1 | 0 | | 0 | 0 | 3 |
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λ=-1: (1,1,0), (-1,0,1),
λ=3: (-1,1,1). |
2.
| A) |
| -1 | 1 | 0 | 0 | | | 0 | -1 | 1 | 0 | | 0 | 0 | -1 | 1 | | 0 | 0 | 0 | -1 |
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, | B) |
| -2 | 1 | 0 | 0 | | | 0 | -2 | 0 | 0 | | 0 | 0 | -2 | 0 | | 0 | 0 | 0 | 3 |
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