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5. Let A be the matrix, 0 1 2 3 0 0 1 2 A o 0 0 4 A is a nilpotent matrix. Look up the definition...

5. Let A be the matrix, 0 1 2 3 0 0 1 2 A o 0 0 4 A is a nilpotent matrix. Look up the definition of a nilpotent matrix and u

5. Let A be the matrix, 0 1 2 3 0 0 1 2 A o 0 0 4 A is a nilpotent matrix. Look up the definition of a nilpotent matrix and use that along with the power series definition of the matrix exponential to find eAt 2!
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The definition of a nilpotent matrix is that , for a square matrix A, there exists a positive integer k, such that

A^k = 0

In this case, we have

3240 2100 1000 4 and

001 10 0 0 0 4 2 and

0 0 0 4

A^4 = 0

In this case, k = 4

Hence using the power series definition

A 12 31

Using the А. Аг. Аз that we got above, we can write

2t 4t2 4t 0 At

This is the answer

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