Matrix
See also: Simultaneous Linear Equations, Geometric Linear Transformation
A matrix is a rectangular array of numbers.
The size of a matrix is its dimension, namely the number of rows and columns of the matrix.
For operations of matrices, please use the two calculators below.
Matrix Addition, Subtraction, and Multiplication
- Enter the dimension of the matrices. (Rows x Columns).
- For multiplication, the number of columns of the first matrix must be equal to the number of rows of the second matrix, ie (a x b)(b x c).
- For addition and subtraction, the dimension of the two matrices must be the same.
- Maximum matrix dimension for this system is 9x9.
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Calculating . . .
Inverse of Matrix
- Enter the dimension of the matrix. (Rows x Columns).
- Maximum matrix dimension for this system is 9x9.
- Result will be rounded to 3 decimal places.
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Calculating . . .
Please report any error to contact@idomaths.com. Thank you.
Matrix Operations
Addition and Subtraction of Matrices
If matrices A and B are of the same size,
- the sum A + B is the matrix obtained by adding the entries of B to the corresponding entries of A.
- the difference A − B is the matrix obtained by subtracting the entries of B from the corresponding entries of A.
| If A = | | and B = | |
| A + B = | |
| A − B = | |
Matrices of different sizes cannot be added or subtracted.
Example
Multiplication of Matrices
If A is an m × r matrix and B is an r × n matrix, the product AB is an m × n matrix whose entry from row i and column j is the sum of the products of the corresponding entries from row i of A and column j of B.
The entry (AB)ij in row i and column j of AB is given by
(AB)ij = ai1b1j + ai2b2j + ai3b3j + … + airbrj
Matrices A and B can only be multiplied if the number of columns of A is the same as the number of rows of B.
Example
- The element at row 1 and column 1 of AB is obtained from summing up the product of corresponding entries of row 1 of A and column 1 of B, i.e.
(AB)11 = (1)(3) + (2)(-1) + (1)(0) = 1
- The element at row 1 and column 2 of AB is obtained from summing up the product of corresponding entries of row 1 of A and column 2 of B, i.e.
(AB)12 = (1)(1) + (2)(2) + (1)(-2) = 3
- The element at row 2 and column 1 of AB is obtained from summing up the product of corresponding entries of row 2 of A and column 1 of B, i.e.
(AB)21 = (0)(3) + (-3)(-1) + (2)(0) = 3
- And so on
See also: Simultaneous Linear Equations, Geometric Linear Transformation
