Question:
If the matrix \(A\) is both symmetric and skew symmetric,then
If the matrix \(A\) is both symmetric and skew symmetric,then
Updated On: Sep 21, 2023
\(A\) is a diagonal matrix
\(A\) is a zero matrix
\(A\) is a square matrix
None of these
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct answer is B:\(A\) is a zero matrix
\(A'=A\,\, and\,\, A'=-A\)
\(\implies A=-A\)
\(\implies A+A=0\)
\(\implies 2A=0\)
\(\implies A=0\)
Therefore, \(A\) is a zero matrix.
\(A'=A\,\, and\,\, A'=-A\)
\(\implies A=-A\)
\(\implies A+A=0\)
\(\implies 2A=0\)
\(\implies A=0\)
Therefore, \(A\) is a zero matrix.
Was this answer helpful?
0
0
Top Questions on Matrices
- Let \( A = \begin{bmatrix} 1 & -2 & -1 \\ 0 & 4 & -1 \\ -3 & 2 & 1 \end{bmatrix}, B = \begin{bmatrix} -5 \\ -2 \end{bmatrix}, C = [9 \ \ 7], \) which of the following is defined?
- If \[ \begin{bmatrix} 4 + x & x - 1 \\ -2 & 3 \end{bmatrix} \] is a singular matrix, then the value of \( x \) is:
If \[ A = \begin{bmatrix} 1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1 \end{bmatrix} \] then find \( A^{-1} \). Hence, solve the system of linear equations: \[ x - 2y = 10, \] \[ 2x - y - z = 8, \] \[ -2y + z = 7. \]
- Find x, y, z if
\[ \begin{bmatrix} 5 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} 0 & 1 & -2 \\ 1 & -2 & 3 \\ -1 & 1 & 1 \end{bmatrix} \begin{bmatrix} x-1 \\ y+1 \\ 2z \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \end{bmatrix}. \] - Solve the following equations by the method of inversion: \( 2x-y+z=1 \), \( x+2y+3z=8 \), \( 3x+y-4z=1 \).
View More Questions
Questions Asked in CBSE CLASS XII exam
- A point charge \( q \) is moving with velocity \( \mathbf{v} \) in a uniform magnetic field \( \mathbf{B} \). Find the work done by the magnetic force on the charge.
- CBSE CLASS XII - 2025
- Moving Charges and Magnetism
- Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]
- CBSE CLASS XII - 2025
- Integration
Assertion (A): The shaded portion of the graph represents the feasible region for the given Linear Programming Problem (LPP).
Reason (R): The region representing \( Z = 50x + 70y \) such that \( Z < 380 \) does not have any point common with the feasible region.
- CBSE CLASS XII - 2025
- Linear Programming Problem
- Find the probability distribution of the number of boys in families having three children, assuming equal probability for a boy and a girl.
- CBSE CLASS XII - 2025
- Probability
- (b) In a village of 8000 people, 3000 go out of the village to work and 4000 are women. It is noted that 30% of women go out of the village to work. What is the probability that a randomly chosen individual is either a woman or a person working outside the village?
- CBSE CLASS XII - 2025
- Probability
View More Questions