The definition of a nilpotent matrix is that , for a square matrix , there exists a positive integer , such that
In this case, we have
and
and
In this case,
Hence using the power series definition
Using the that we got above, we can write
This is the answer
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...