Question:
Let X be a matrix of order $2 \times n$ and Z be a matrix of order $2 \times p$. If n = p, then the order of the matrix $7X - 5Z$ is
Let X be a matrix of order $2 \times n$ and Z be a matrix of order $2 \times p$. If n = p, then the order of the matrix $7X - 5Z$ is
Updated On: Jul 6, 2022
- $p \times 2 $
- $2 \times n$
- $n \times 3 $
- $p \times n $
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The Correct Option is B
Solution and Explanation
The order of matrix X is $2 \times n$, The order of matrix Z is $2 \times p$
7X - 5Z is defined when X and Z of the same order $\Rightarrow \, n = p$
Thus the order of 7X - 5Z is $2 \times n$.
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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.