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...

Question

Question

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

Answer 1

Answer #1

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

Answer 2

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