The number of all possible matrices of order 3 $\times$ 3 with each entry 0 or 1 is
- 18
- 512
- 81
- none of these
The Correct Option is B
Solution and Explanation
Top Questions on matrix transformation
A, B, C, D are square matrices such that A + B is symmetric, A - B is skew-symmetric, and D is the transpose of C.
If
\[ A = \begin{bmatrix} -1 & 2 & 3 \\ 4 & 3 & -2 \\ 3 & -4 & 5 \end{bmatrix} \]
and
\[ C = \begin{bmatrix} 0 & 1 & -2 \\ 2 & -1 & 0 \\ 0 & 2 & 1 \end{bmatrix} \]
then the matrix \( B + D \) is:
- TS EAMCET - 2024
- Mathematics
- matrix transformation
Given matrices \( A \) and \( B \) where:
\[ A = \begin{bmatrix} 1 & 2 \\ 2 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} x & y \\ 1 & 2 \end{bmatrix} \]and the condition:
\[ (A + B)(A - B) = A^2 - B^2 \]If matrix \( C \) is defined as:
\[ C = \begin{bmatrix} x & 2 \\ 1 & y \end{bmatrix} \]then the trace of \( C \) is:
\[ \text{Tr}(C) = x + y \]- TS EAMCET - 2024
- Mathematics
- matrix transformation
- \(\frac{1}{3.6} + \frac{1}{6.9} + \frac{1}{9.12} + \dots\) up to 9 terms \(=\)
- TS EAMCET - 2024
- Mathematics
- matrix transformation
Matrix Inverse Sum Calculation
Given the matrix:
A = | 1 2 2 | | 3 2 3 | | 1 1 2 |
The inverse matrix is represented as:
A-1 = | a11 a12 a13 | | a21 a22 a23 | | a31 a32 a33 |
The sum of all elements in A-1 is:
∑ aij = 3
- TS EAMCET - 2024
- Mathematics
- matrix transformation
Calculate the determinant of the matrix:
- TS EAMCET - 2024
- Mathematics
- matrix transformation
Concepts Used:
Matrix Transformation
The numbers or functions that are kept in a matrix are termed the elements or the entries of the matrix.
Transpose Matrix:
The matrix acquired by interchanging the rows and columns of the parent matrix is termed the Transpose matrix. The definition of a transpose matrix goes as follows - “A Matrix which is devised by turning all the rows of a given matrix into columns and vice-versa.”