## Matrices

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### M1 Matrices: Introduction

A matrix is an array of numbers. This module discusses matrices, their order, row and column matrices, square matrices and the identity matrix.

### M10 Eigenvalues and eigenvectors

Eigenvalues and eigenvectors are used to understand how buildings, structures and automobiles react in real life. They also provide insights into many mathematical areas.

### M2 Addition and subtraction of matrices

Matrices of the same shape (same number of rows and columns) may be added/subtracted by adding/subtracting the corresponding elements.

### M3 Matrix multiplication

To multiply two matrices A and B, the number of columns in A must equal the number of rows in B.

### M4 Determinant of a matrix

The determinant of a matrix can only be calculated for a square matrix and is used in many aspects of mathematics/engineering/physics.

### M6 Systems of equations

Systems of linear equations may be solved using elementary row operations. This is sometimes called Gaussian elimination.

### M7 Types of solutions

Systems of linear equations can have infinitely many solutions, no solution, or a unique solution.

### M8 Inverse of a 2x2 matrix

There is no division operation in matrix algebra. However, there is multiplication by the inverse.