Question:
If A is symmetric as well as skew-symmetric matrix, then A is
If A is symmetric as well as skew-symmetric matrix, then A is
Updated On: Jul 6, 2022
- Diagonal
- null zero matrix
- Triangular
- None of these
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The Correct Option is B
Solution and Explanation
Let $A = [a_{ij}]_{nxm}$. Since A is skew-symmetric
$a_{ii} = 0 (i = 1, 2, ......, n)$ and $a_{ji} = - a_{ji} (i \neq j)$
Also, A is symmetric so $a_{ji} = a_{ji} \, \forall $ i and j
$\therefore \, a_{ji} = 0 \, \forall \, i \neq j$
Hence $a_{ij} = 0 \, \forall \, i $ and $j \, \Rightarrow \, A$ is a null zero matrix
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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.