Question:
In the matrix A= \(\begin{bmatrix} 2 & 5 & 19&-7 \\ 35 & -2 & \frac{5}{2}&12 \\ \sqrt3 & 1 & -5&17 \end{bmatrix}\),write:
I. The order of the matrix
II. The number of elements
III. Write the elements a13, a21, a33, a24, a23
In the matrix A= \(\begin{bmatrix} 2 & 5 & 19&-7 \\ 35 & -2 & \frac{5}{2}&12 \\ \sqrt3 & 1 & -5&17 \end{bmatrix}\),write:
I. The order of the matrix
II. The number of elements
III. Write the elements a13, a21, a33, a24, a23
Updated On: Mar 2, 2024
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Solution and Explanation
(i) In the given matrix, the number of rows is 3 and the number of columns is 4.
Therefore, the order of the matrix is 3 × 4.
(ii) Since the order of the matrix is 3 × 4, there are 3 × 4 = 12 elements in it.
(iii) \(a_{13}=19, a_{21}=35,a_{33}=-5,a_{24}=12,a_{23}=\frac{5}{2}\)
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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.