Matrix operations are fundamental in linear algebra and are widely used in various fields such as physics, engineering, and computer graphics. In this tutorial, we will cover the basic operations of matrices, including addition, subtraction, multiplication, and division.

Matrix Addition

Matrix addition is performed by adding corresponding elements of two matrices. The matrices must be of the same size.

  • Example:
    • Matrix A:
      1 2
3 4
    • Matrix B:
      5 6
7 8
    • Result:
      6 8
10 12

Matrix Subtraction

Matrix subtraction is similar to matrix addition, but we subtract the corresponding elements of two matrices.

  • Example:
    • Matrix A:
      1 2
3 4
    • Matrix B:
      5 6
7 8
    • Result:
      -4 -4
-4 -4

Matrix Multiplication

Matrix multiplication is more complex and involves multiplying rows of the first matrix with columns of the second matrix.

  • Example:
    • Matrix A:
      1 2
3 4
    • Matrix B:
      5 6
7 8
    • Result:
      19 22
43 50

For more information about matrix operations, you can visit our Matrix Operations Guide.

Matrix Division

Matrix division is not the same as matrix multiplication. Instead, it involves finding the inverse of a matrix and then multiplying it by the inverse of the other matrix.

  • Example:
    • Matrix A:
      1 2
3 4
    • Inverse of Matrix A:
      -2 1
1.5 -0.5
    • Result:
      -3.5 0.5
1.5 -0.5

For further reading, check out our Matrix Inversion Tutorial.