Lf - 2 4- -1 k - is an nilpotent matrix of index 2- then k-

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Finding Inverse Using Elementary Transformations

lf [ 2 4; -...

Question

lf $(\begin{matrix} 2 & 4 - 1 & k \end{matrix})$ is an nilpotent matrix of index 2, then $k =$

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

2,

k

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & - 3 & - 4 - 1 & 3 & 4 1 & - 3 & - 4 \end{matrix} ⎤ ⎥ ⎦

2

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

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

A = [\begin{matrix} a b & b^{2} {- a}^{2} & - a b \end{matrix}]

2

A^{2} = A . A = [\begin{matrix} a^{2} b^{2} - & a^{2} b^{2} {- a}^{3} b + & a^{3} b \end{matrix} \begin{matrix} a b^{3} - & {a b}^{3} {- a}^{2} b^{2} + & a^{2} b^{2} \end{matrix}]

[\begin{matrix} 0 & 0 0 & 0 \end{matrix}] = O

A

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