Matrices are fundamental mathematical concepts used in many areas of science, engineering, and computer science. Matrices are often used to represent and solve systems of linear equations, perform transformations, and analyze data. This tutorial covers the basics of matrices, including definitions, notations, and operations.
Definition: A matrix is a rectangular array of numbers arranged in rows and columns. For example, here is an example of a 2x3 matrix:
[ 2 3 1 ]
[ 0 1 4 ]
This matrix has two rows and three columns.
Notation:
matrices are usually written with uppercase letters such as A, B, or C. Individual elements of the matrix are indicated by lowercase letters and have subscripts indicating their position in rows and columns. For example, the elements of the first row and second column of matrix A are denoted by index A with index A₁₂.
Operations:
Matrices can be added and multiplied by other matrices, and can also be multiplied by scalar values. Here are the basic matrix operations.
Add Matrices: Two matrices can be added if they have the same dimension.
The sum of two matrices A and B is denoted A + B and is obtained by adding their elements.
Matrix Multiplication: Two matrices can be multiplied if the number of columns in the first matrix equals the number of rows in the second matrix. The product of two matrices A and B, denoted by AB, is obtained by multiplying their elements.
Dot Multiply: Allows a matrix to be multiplied by a single number, a scalar value. The product of a scalar value k and a matrix A is denoted by kA and is obtained by multiplying each element of the matrix by a scalar value.
Transpose: The transpose of a matrix is done by swapping rows and columns. The transpose of matrix A is denoted by A^T.
- WORK SHEET 1
- WORK SHEET 2
- WORK SHEET 3
- WORK SHEET 4
- WORK SHEET 5
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