Equality of two matrix: Two matrices [a_{ij}] and [b_{ij}] are said to be equal when they have the same number of rows and columns and a_{ij} = b_{ij} for all admissible values of i and j.
Definition of Equal Matrices:
Two matrices A and B are said to be equal if A and B have the same order and their corresponding elements be equal. Thus if A = (a_{ij})_{m,n} and B = (b_{ij})_{m,n} then A = B if and only if a_{ij} = b_{ij} for i = 1, 2, 3, ....., m; j = 1, 2, 3, ......., n.
The number of rows in matrix A = The number of rows in matrix B and The number of columns in matrix A = The number of columns in matrix B
Corresponding elements of the matrix A and the matrix B are equal that is the entries of the matrix A and the matrix B in the same position are equal.
Otherwise, the matrix A and the matrix B are said to be unequal matrix and we represent A ≠ B.
Examples of Equal Matrices:
1. The matrices A = \(\begin{bmatrix} 5 \end{bmatrix}\) and B = \(\begin{bmatrix} 5 \end{bmatrix}\) are equal, because both matrices are of the same order 1 × 1 and their corresponding entries are equal.
2. The matrices A = \(\begin{bmatrix} 2 & 7\\ 3 & 1 \end{bmatrix}\) and B = \(\begin{bmatrix} 2 & 7\\ 3 & 1 \end{bmatrix}\) are equal, because both matrices are of the same order 2 × 2 and their corresponding entries are equal.
3. The matrices A = \(\begin{bmatrix} 4 & 6 & 1\\ 2 & 5 & 9\\ 7 & 0 & 3 \end{bmatrix}\) and B = \(\begin{bmatrix} 4 & 6 & 1\\ 2 & 5 & 9\\ 7 & 0 & 3 \end{bmatrix}\) are equal, because both matrices are of the same order 3 × 3 and their corresponding entries are equal.
4. The matrices A = \(\begin{bmatrix} 2 & 1 & 6 & 5\\ 5 & 4 & 3 & 3\\ 7 & 7 & 9 & 5\\ 2 & 3 & 8 & 4 \end{bmatrix}\) and B = \(\begin{bmatrix} 2 & 1 & 6 & 5\\ 5 & 4 & 3 & 3\\ 7 & 7 & 9 & 5\\ 2 & 3 & 8 & 4 \end{bmatrix}\) are equal, because both matrices are of the same order 4 × 4 and their corresponding entries are equal.
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