text If A - Wegin bmatrix 1 - 2 - 1110 -1 -1110 - 0 - 1lendbmatrix - - text then - A -100-A- IB- 50 IC- AD- 100 I

The correct option is A IA^2=[ 1 amp; 2 amp; 1; 0 amp; 1 amp; 1; 0 amp; 0 amp; 1 nbsp; ][ 1 amp; 2 amp; 1; 0 amp; 1 am ...

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Standard XII

Mathematics

Transpose of a Matrix

text If A = W...

Question

$If A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & - 1 & - 1 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦, then A^{100} =$

I

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Solution

The correct option is A $I$
$A^{2} = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & - 1 & - 1 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & - 1 & - 1 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = I A^{100} = (A^{2})^{50} = I^{50} = I$

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If A=⎡⎢⎣1210−1−1001⎤⎥⎦, then A100=

The correct option is A IA2=⎡⎢⎣1210−1−1001⎤⎥⎦⎡⎢⎣1210−1−1001⎤⎥⎦=⎡⎢⎣100010001⎤⎥⎦=IA100=(A2)50=I50=I

$If A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & - 1 & - 1 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦, then A^{100} =$