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Matrix AdditionCalculator

Matrix size: x





Answer




How to use this Matrix Addition Calculator 🤔

Follow these steps to perform Matrix Addition for the given matrices.

  1. Enter the matrix size for matrix A, and matrix B.
  2. Based on the given matrix size, a matrix of input fields appears. Enter the matrix elements.
  3. As and when you complete entering the matrix elements, Matrix Addition is calculated, and displayed in the answer section.

Matrix Addition

Matrix addition is the process of adding two matrices by adding their corresponding elements. This operation is only possible when the matrices have the same dimensions.

Given two matrices A and B, their sum C = A + B is computed as:


C[i][j] = A[i][j] + B[i][j]

where 1 ≤ i ≤ m and 1 ≤ j ≤ n, and m and n are the number of rows and columns of the matrices, respectively.

Example 1

Let's add the following two matrices:

\( A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \)

\( B = \begin{bmatrix} 4 & 5 & 6 \\ 7 & 8 & 9 \\ 1 & 2 & 3 \end{bmatrix} \)

The sum of A and B is:

\( C = A + B = \begin{bmatrix} 1+4 & 2+5 & 3+6 \\ 4+7 & 5+8 & 6+9 \\ 7+1 & 8+2 & 9+3 \end{bmatrix} = \begin{bmatrix} 5 & 7 & 9 \\ 11 & 13 & 15 \\ 8 & 10 & 12 \end{bmatrix} \)

Example 2

Consider another example with different matrices:

\( A = \begin{bmatrix} 2 & 4 \\ 6 & 8 \end{bmatrix} \)

\( B = \begin{bmatrix} 1 & 3 \\ 5 & 7 \end{bmatrix} \)

The sum of A and B is:

\( C = A + B = \begin{bmatrix} 2+1 & 4+3 \\ 6+5 & 8+7 \end{bmatrix} = \begin{bmatrix} 3 & 7 \\ 11 & 15 \end{bmatrix} \)

These examples demonstrate the basic process of matrix addition by adding corresponding elements of the input matrices to get the resultant matrix.