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3 and 4 .Determinants and Matrices
normal
જો $A = \left[ {\begin{array}{*{20}{c}}
1&0\\
{\frac{1}{2}}&1
\end{array}} \right]$ , તો $A^{50}$ મેળવો.
A
$\left[ {\begin{array}{*{20}{c}} 1&{25}\\ 0&1 \end{array}} \right]$
B
$\left[ {\begin{array}{*{20}{c}} 1&0\\ {25}&1 \end{array}} \right]$
C
$\left[ {\begin{array}{*{20}{c}} 1&0\\ 0&{50} \end{array}} \right]$
D
$\left[ {\begin{array}{*{20}{c}} 1&0\\ {50}&1 \end{array}} \right]$
Solution
If we calculate $A^{2}=\left[\begin{array}{cc}{1} & {0} \\ {2\left(\frac{1}{2}\right)} & {1}\end{array}\right]$
$A^{3}=\left[\begin{array}{cc}{1} & {0} \\ {3\left(\frac{1}{2}\right)} & {1}\end{array}\right], \ldots \ldots \ldots, A^{50}=\left[\begin{array}{cc}{1} & {0} \\ {50\left(\frac{1}{2}\right)} & {1}\end{array}\right]$
Standard 12
Mathematics
