Question:
If $A = [a_{ij}]_{m \times n}$ be a scalar matrix, then trace of $A$ is equal to
If $A = [a_{ij}]_{m \times n}$ be a scalar matrix, then trace of $A$ is equal to
Updated On: Jul 6, 2022
- n
- 0
- $na_{11}$
- none of these
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The Correct Option is C
Solution and Explanation
Trace of A is equal to the sum of diagonal elements of A
$ = a_{11} + a_{22}+a_{33} + .... +a_{nn}$
$ = na_{11} $
($\because$ all the diagonal elements of a scalar matrix are equal, $\therefore a_{11} = a_{22} = a_{33} = ... = a_{nn}$)
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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.