If $ A=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right], $ then $ (A-A') $ is equal to (where, $A'$ is transpose of matrix $A$)
- null matrix
- identity matrix
- symmetric
- skew-symmetric
The Correct Option is D
Solution and Explanation
The correct option is(D): skew-symmetric.
Given, \(A=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right]\)
Then, \(A'=\left[ \begin{matrix} 3 & 1 \\ -4 & -1 \\ \end{matrix} \right]\)
Now, \(A-A'=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right]-\left[ \begin{matrix} 3 & 1 \\ -4 & -1 \\ \end{matrix} \right]\)
\(\Rightarrow\) \(A-A'=\left[ \begin{matrix} 0 & -5 \\ 5 & 0 \\ \end{matrix} \right]\) .. (i)
Now, we have \(A'-A=\left[ \begin{matrix} 3 & 1 \\ -4 & -1 \\ \end{matrix} \right]-\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right]=\left[ \begin{matrix} 0 & 5 \\ -5 & 0 \\ \end{matrix} \right]\)
\(\Rightarrow\) \((A'-A)'=\left[ \begin{matrix} 0 & -5 \\ 5 & 0 \\ \end{matrix} \right]=(A-A')\)
[From E (i)] which represent that \((A-A')\) is skew-symmetric matrix.
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:
Questions Asked in JKCET exam
- A moving block having mass $m$, collides with another stationary block having mass $4\,m$. The lighter block comes to rest after collision. When the initial velocity of the lighter block is $v$, then the value of coefficient of restitution (e) will be
- JKCET - 2019
- work, energy and power
- A force $ F = 3x^2 + 2x + 1 $ acts on a body in the $ x $ -direction. The work done by this force during a displacement from $ x = -1 $ to $ +1 $ is
- JKCET - 2019
- work, energy and power
- What is the colour of the flame on heating potassium in the flame of a Bunsen burner?
- JKCET - 2019
- GROUP 1 ELEMENTS
- If $ a $ , $ b $ , $ c $ are the lengths of three edges of unit cell, $ \alpha $ is the angle between side $ b $ and $ c $ , $ \beta $ is the angle between side $ a $ and $ c $ and $ \gamma $ is the angle between side $ a $ and $ b $ , what is the Bravais Lattice dimensions of a tetragonal crystal?
- JKCET - 2019
- The solid state
- Which of the following compounds is known as copper glance?
- JKCET - 2019
- General Principles and Processes of Isolation of Elements
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.