Question:
If $A = \begin{bmatrix}\cos\alpha&\sin\alpha\\ - \sin\alpha&\cos\alpha\end{bmatrix}$ , then $AA' = $
If $A = \begin{bmatrix}\cos\alpha&\sin\alpha\\ - \sin\alpha&\cos\alpha\end{bmatrix}$ , then $AA' = $
Updated On: May 22, 2024
- A
- Zero matrix
- A'
- I
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
$AA' = \begin{bmatrix}\cos\alpha&\sin\alpha\\ - \sin\alpha&\cos\alpha\end{bmatrix} \begin{bmatrix}\cos\alpha&-\sin\alpha\\ \sin\alpha&\cos\alpha\end{bmatrix}$
$ = \begin{bmatrix} 1 &0\\ 0 & 1 \end{bmatrix} = I $
$ = \begin{bmatrix} 1 &0\\ 0 & 1 \end{bmatrix} = I $
Was this answer helpful?
1
0
Top Questions on Matrices
- If \(A = \begin{bmatrix} 3 & 2 \\ -1 & 1 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} -1 & 0 \\ 2 & 5 \\ 3 & 4 \end{bmatrix},\)then \((BA)^T\) is equal to:
- If \( A = \begin{bmatrix} K & 4 \\ 4 & K \end{bmatrix} \) and \( |A^3| = 729 \), then the value of \( K^8 \) is:
- Let $A$ be a matrix such that $A^2 = I$, where $I$ is an identity matrix. Then $(I + A)^4 - 8A$ is equal to:
- Let $A = I_2 - MM^T$, where $M$ is a real matrix of order $2 \times 1$ such that the relation $M^T M = I_1$ holds. If $\lambda$ is a real number such that the relation $AX = \lambda X$ holds for some non-zero real matrix $X$ of order $2 \times 1$, then the sum of squares of all possible values of $\lambda$ is equal to:
- Let the system of equations \[x + 2y + 3z = 5, \quad 2x + 3y + z = 9, \quad 4x + 3y + \lambda z = \mu\]have an infinite number of solutions. Then $\lambda + 2\mu$ is equal to:
View More Questions
Questions Asked in KCET exam
- Ten identical cells each emf 2V and internal resistance 1Ω are connected in series with two cells wrongly connected. A resistor of 10Ω is connected to the combination. What is the current through the resistor?
- KCET - 2023
- Cells in Series and in Parallel
- The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is vrms. The ratio of the velocities v and vrms for helium and oxygen gases are X and X' respectively. Then \(\frac{X}{X'}\) is equal to
- KCET - 2023
- Thermodynamics
- If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
- KCET - 2023
- Arithmetic Progression
- A stretched wire of a material whose Young's modulus Y = 2 × 1011 Nm-2 has Poisson's ratio of 0.25. Its lateral strain εl = 10-3. The elastic energy density of the wire is
- KCET - 2023
- mechanical properties of solids
- A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field BH = 3 × 10-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms-2 )
- KCET - 2023
- Faradays laws of induction
View More Questions
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.