Equal Matrices

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.

10th Grade Math

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