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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.
M5 Special matrices
It is helpful to understand the definition of a number of different types of “special” matrices.
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.