Question:
The number of $3 \times 3$ non-singular matrices, with four entries as $ 1 $ and all other entries as $0$, is
The number of $3 \times 3$ non-singular matrices, with four entries as $ 1 $ and all other entries as $0$, is
Updated On: Jul 5, 2022
- 5
- 6
- at least 7
- less than 4
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The Correct Option is C
Solution and Explanation
First row with exactly one zero; total number of cases = 6
First row 2 zeros we get more cases
Total we get more than 7.
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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.