Question:
The number of all possible matrices of order 2 x 2 with each entry 0 or 1 is:
The number of all possible matrices of order 2 x 2 with each entry 0 or 1 is:
Updated On: Jan 3, 2024
- 27
- 18
- 16
- 81
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Four elements overall are contained in a \(2 × 2\) matrix.
Either \(1\) or \(0\) can be used in place of each element.
Each of the four spaces can therefore be filled in one of two ways.
Therefore, there will be a total of \(2×2×2×2 = 2^4\) matrices in this type of matrix.
Consequently, \(16\) is the maximum number of \(2\times2\) order matrices that can have either \(0\) or \(1\) for each entry.
Was this answer helpful?
0
0
Top Questions on Matrices
- Let \( A = \begin{bmatrix} 2 & 0 \\ 0 & 3 \end{bmatrix} \). The determinant of \( A^3 \) is:
- Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.
- The matrix $A = \begin{pmatrix} \sqrt{3} & 0 & 0 \\ 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{5} \end{pmatrix}$ is a/an :
- If \[ \begin{bmatrix} 3 & -1 \\ 0 & 1 \\ 2 & -3 \end{bmatrix} A = \begin{bmatrix} 2 & -5 \\ -17 \end{bmatrix} \] then find matrix \( A \).
- If \[ \begin{bmatrix} 2x-1 & 3x \\ 0 & y^2-1 \end{bmatrix} = \begin{bmatrix} x+3 & 12 \\ 0 & 35 \end{bmatrix} \] then the value of \( (x - y) \) is :
View More Questions
Questions Asked in CUET exam
- Which region was known as the ‘nursery of the Bengal Army’ as many sepoys were recruited from there?
- CUET (UG) - 2025
- British Empire
- A shopkeeper increases the price of an article by 25% and then offers a discount of 20%. What is the net percentage change in the price?
- CUET (UG) - 2025
- Percentage
- In a certain code, WATER is written as YCVGT. How is HOUSE written?
- CUET (UG) - 2025
- Coding Decoding
- A person walks 10 m North, then turns right and walks 5 m, then turns right again and walks 10 m. What direction is he facing now?
- CUET (UG) - 2025
- Direction sense
- A and B can complete a task in the ratio 3:2. If together they complete the task in 20 days, how long will A alone take?
- CUET (UG) - 2025
- Time and Work
View More Questions
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.