Order of Matrices: Two matrices are said to be equal if they have the same dimensions and the corresponding elements are equal. In other words, if we have t...
Order of Matrices:
Two matrices are said to be equal if they have the same dimensions and the corresponding elements are equal. In other words, if we have two matrices A and B with dimensions m x n and m' x n', respectively, then A = B if m = m' and n = n'.
Equality of Matrices:
Two matrices A and B are equal if they have the same dimensions and the corresponding elements are equal. This means that each element in the matrix A is equal to the corresponding element in matrix B, and vice versa.
Examples:
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |
and
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |
are equal matrices.
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |
and
| 1 2 3 |
| 5 6 7 |
| 8 9 10 |
are not equal matrices.
Order of matrices is a specific arrangement of elements in a matrix. For example, the order of the rows of a matrix is not the same as the order of the columns.
Order and dimension are independent concepts. Two matrices with the same dimensions can be equal even if they have different orders. For instance:
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |
and
| 1 2 3 |
| 4 5 6 |
| 7 8 9 |
are equal matrices, even though their orders are different