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STD 12 - 3 and 4 . determinant and metrices — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 3 and 4 . determinant and metrices1 Mark
MCQ
If $A = \left[ {\begin{array}{*{20}{c}}
1&0\\
{\frac{1}{2}}&1
\end{array}} \right]$ , then $A^{50}$ is
  • A
    $\left[ {\begin{array}{*{20}{c}}
    1&{25}\\
    0&1
    \end{array}} \right]$
  • ✓
    $\left[ {\begin{array}{*{20}{c}}
    1&0\\
    {25}&1
    \end{array}} \right]$
  • C
    $\left[ {\begin{array}{*{20}{c}}
    1&0\\
    0&{50}
    \end{array}} \right]$
  • D
    $\left[ {\begin{array}{*{20}{c}}
    1&0\\
    {50}&1
    \end{array}} \right]$
✓

Answer

Correct option: B.
$\left[ {\begin{array}{*{20}{c}}
1&0\\
{25}&1
\end{array}} \right]$
b
If we calculate $A^{2}=\left[\begin{array}{cc}{1} & {0} \\ {2\left(\frac{1}{2}\right)} & {1}\end{array}\right]$

$A^{3}=\left[\begin{array}{cc}{1} & {0} \\ {3\left(\frac{1}{2}\right)} & {1}\end{array}\right], \ldots \ldots \ldots, A^{50}=\left[\begin{array}{cc}{1} & {0} \\ {50\left(\frac{1}{2}\right)} & {1}\end{array}\right]$

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