The number of all possible matrices of order 2 x 2 with each entry 0 or 1 is:
- 27
- 18
- 16
- 81
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.
Top Questions on Matrices
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- Find x, y, z if
\[ \begin{bmatrix} 5 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} 0 & 1 & -2 \\ 1 & -2 & 3 \\ -1 & 1 & 1 \end{bmatrix} \begin{bmatrix} x-1 \\ y+1 \\ 2z \end{bmatrix} = \begin{bmatrix} 2 \\ 1 \end{bmatrix}. \]
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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.