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
- Four friends Abhay, Bina, Chhaya, and Devesh were asked to simplify \( 4 AB + 3(AB + BA) - 4 BA \), where \( A \) and \( B \) are both matrices of order \( 2 \times 2 \). It is known that \( A \neq B \) and \( A^{-1} \neq B \). Their answers are given as:
- Given \[ A = \begin{bmatrix} -4 & 4 & 4 \\ -7 & 1 & 3 \\ 5 & -3 & -1 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & 3 \end{bmatrix} \] find \( AB \). Hence, solve the system of linear equations: \[ x - y + z = 4, \] \[ x - 2y - 2z = 9, \] \[ 2x + y + 3z = 1. \]
- If \[ A = \begin{bmatrix} 1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1 \end{bmatrix} \] then find \( A^{-1} \). Hence, solve the system of linear equations: \[ x - 2y = 10, \] \[ 2x - y - z = 8, \] \[ -2y + z = 7. \]
- Assertion (A): \( A = \text{diag} [3, 5, 2] \) is a scalar matrix of order \( 3 \times 3 \).
Reason (R): If a diagonal matrix has all non-zero elements equal, it is known as a scalar matrix. - If \( A \) and \( B \) are square matrices of order \( m \) such that \( A^2 - B^2 = (A - B)(A + B) \), then which of the following is always correct?
View More Questions
Questions Asked in CUET exam
- Match the words in List-I with their definitions in List-II :
List-I (Words) List-II (Definitions) (A) Theocracy (I) One who keeps drugs for sale and puts up prescriptions (B) Megalomania (II) One who collects and studies objects or artistic works from the distant past (C) Apothecary (III) A government by divine guidance or religious leaders (D) Antiquarian (IV) A morbid delusion of one’s power, importance or godliness Choose the correct answer from the options given below :- CUET (UG) - 2024
- Vocabulary
- Complete the sentences given in List-I with the appropriate prepositions given in List-II:
- The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$ are $A(0, 8)$, $B(4, 0)$, and $C(8, 0)$. If the objective function $Z = ax + by$ has its maximum value on the line segment $AB$, then the relation between $a$ and $b$ is:
- CUET (UG) - 2024
- Linear Programmig Problem
- Identify the correct sequence of the Selection process:
(A) Selection decision
(B) Employment interview
(C) Selection tests
(D) Reference checking- CUET (UG) - 2024
- Staffing
- If \(\tan^{-1}\left(\frac{2}{3 - x + 1}\right) = \cot^{-1}\left(\frac{3}{3x + 1}\right)\), then which one of the following is true?
- CUET (UG) - 2024
- Inverse Trigonometric Functions
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.