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Q.If A=(111 011 001)A = \begin{pmatrix} 1 & 1 & 1 \ 0 & 1 & 1 \ 0 & 0 & 1 \end{pmatrix}, then A50A^{50} equals

a
(1501225 0150 001)\begin{pmatrix} 1 & 50 & 1225 \ 0 & 1 & 50 \ 0 & 0 & 1 \end{pmatrix}
b
(1501275 0150 001)\begin{pmatrix} 1 & 50 & 1275 \ 0 & 1 & 50 \ 0 & 0 & 1 \end{pmatrix}
c
(101225 0150 001)\begin{pmatrix} 1 & 0 & 1225 \ 0 & 1 & 50 \ 0 & 0 & 1 \end{pmatrix}
d
(15050 0150 001)\begin{pmatrix} 1 & 50 & 50 \ 0 & 1 & 50 \ 0 & 0 & 1 \end{pmatrix}

Correct Answer: Option A

The correct solution involves applying the fundamental concept to derive the final value step by step...

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