JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A = \,\left[ {\begin{array}{*{20}{c}}
1&0&0\\
1&1&0\\
1&1&1
\end{array}} \right]\) and \(B = A^{20}\) . Then the sum of the elements of the first column of \(B\) is?
- A \(211\)
- B \(210\)
- C \(231\)
- D \(251\)
Answer & Solution
Correct Answer
(C) \(231\)
Step-by-step Solution
Detailed explanation
Here \(A = \left[ {\begin{array}{*{20}{c}} 1&0&0\\ 1&1&0\\ 1&1&1 \end{array}} \right]\) \(\therefore {A^2} = A.A = \left[ {\begin{array}{*{20}{c}} 1&0&0\\ 1&1&0\\ 1&1&1 \end{array}} \right] \times \left[ {\begin{array}{*{20}{c}} 1&0&0\\ 1&1&0\\ 1&1&1 \end{array}} \right]\)…
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