JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[a_{i j}\right]\) be a matrix of order \(3 \times 3\), with \(a_{i j}=(\sqrt{2})^{i+j}\). If the sum of all the elements in the third row of \(A^2\) is \(\alpha+\beta \sqrt{2}, \alpha, \beta \in \mathbf{Z}\), then \(\alpha+\beta\) is equal to :
- A 280
- B 224
- C 210
- D 168
Answer & Solution
Correct Answer
(B) 224
Step-by-step Solution
Detailed explanation
\begin{aligned} & A=\left[\begin{array}{lll}(\sqrt{2})^2 & (\sqrt{2})^3 & (\sqrt{2})^4 \\ (\sqrt{2})^3 & (\sqrt{2})^4 & (\sqrt{2})^5 \\ (\sqrt{2})^4 & (\sqrt{2})^5 & (\sqrt{2})^6\end{array}\right] \\ & A=\left[\begin{array}{ccc}2 & 2 \sqrt{2} & 4 \\ 2 \sqrt{2} & 4 & 4 \sqrt{2}…
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