Question:
If the matrix $A=\begin{pmatrix}2&0&0\\ 0&2&0\\ 2&0&2\end{pmatrix},$ then $A^{n}=\begin{pmatrix}a&0&0\\ 0&a&0\\ b&0&a\end{pmatrix}, n\,\in\,N$ where
If the matrix $A=\begin{pmatrix}2&0&0\\ 0&2&0\\ 2&0&2\end{pmatrix},$ then $A^{n}=\begin{pmatrix}a&0&0\\ 0&a&0\\ b&0&a\end{pmatrix}, n\,\in\,N$ where
Updated On: Feb 2, 2024
- $a = 2n, b = 2^n$
- $a = 2^n, b = 2n$
- $a = 2^n, b = n^{2n-1}$
- $a = 2^n, b = n2^n$
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The Correct Option is D
Solution and Explanation
$A=2\begin{pmatrix}1&0&0\\ 0&1&0\\ 1&0&1\end{pmatrix} \Rightarrow A^{n}=2^{n}\begin{pmatrix}1&0&0\\ 0&1&0\\ n&0&1\end{pmatrix}$
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Concepts Used:
Matrices
Matrix:
A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for the operations like subtraction, addition, and multiplications. The size of a matrix is determined by the number of rows and columns in the matrix.
The basic operations that can be performed on matrices are:
- Addition of Matrices - The addition of matrices addition can only be possible if the number of rows and columns of both the matrices are the same.
- Subtraction of Matrices - Matrices subtraction is also possible only if the number of rows and columns of both the matrices are the same.
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