Question:
If $M=\begin{pmatrix}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{pmatrix}$, then which of the following matrices is equal to $M^{2022}$ ?
If $M=\begin{pmatrix}\frac{5}{2} & \frac{3}{2} \\ -\frac{3}{2} & -\frac{1}{2}\end{pmatrix}$, then which of the following matrices is equal to $M^{2022}$ ?
Updated On: Aug 11, 2024
\(\begin{pmatrix}3034 & 3033 \\ -3033 & -3032\end{pmatrix}\)
\(\begin{pmatrix}3034 & 3033 \\ -3033 & -3032\end{pmatrix}\)
- $\begin{pmatrix}3034 & -3033 \\ 3033 & -3032\end{pmatrix}$
- $\begin{pmatrix}3033 & 3032 \\ -3032 & -3031\end{pmatrix}$
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The Correct Option is A
Solution and Explanation
So, the correct option is (A): \(\begin{pmatrix}3034 & 3033 \\ -3033 & -3032\end{pmatrix}\)
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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.
- Scalar Multiplication - The product of a matrix A with any number 'c' is obtained by multiplying every entry of the matrix A by c, is called scalar multiplication.
- Multiplication of Matrices - Matrices multiplication is defined only if the number of columns in the first matrix and rows in the second matrix are equal.
- Transpose of Matrices - Interchanging of rows and columns is known as the transpose of matrices.