Question:
Let $A=(a_{ij})_{m\times n}$ be a matrix such that $a_{ij}=1$ for all I, j. Then
Let $A=(a_{ij})_{m\times n}$ be a matrix such that $a_{ij}=1$ for all I, j. Then
Updated On: Jul 6, 2022
- rank (A) > 1
- rank (A) = 1
- rank (A) = m
- rank (A) = n
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The Correct Option is B
Solution and Explanation
Rank A = 1
[$\therefore$ every minor of order 2 = 0 and there exists at least one minor of order 1 which is $\neq$ 0 since $a_{ij}$ = 1 for all i,j]
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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.