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Square Matrix

14. What is n...

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14. What is nilpotent matrix?

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Q. A square matrix A is said to be a nilpotent matrix of degree

r

r

is the least positive integer such that

A^{r} = 0

A

B

are nilpotent matrices then

A + B

will be a nilpotent matrix if

$A = [\begin{matrix} 2 & 4 - 1 & - 2 \end{matrix}]$ is a nilpotent matrix.

Q. The order of nilpotent matrix

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 3 5 & 2 & 6 - 2 & - 1 & - 3 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 3 5 & 2 & 6 - 2 & - 1 & - 3 \end{matrix} ⎤ ⎥ ⎦

is nilpotent matrix of order

3

(\begin{matrix} 2 & 4 - 1 & k \end{matrix})

is an nilpotent matrix of index 2, then

k =

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