All Learning Graphs

Matrix equations & systems of linear equations

The purpose of this learning graph is, on the one hand, to solve matrix equations and, on the other hand, to solve systems of linear equations, Matrices are the perfect tool for solving systems of equations. A very concise way of writing a system of linear equations is using the matrix equation: $A X = B$, where $A$ is an $n × m$ matrix, $X$ is an $m × 1$ matrix and $B$ is an $n × 1$ matrix.
# Equations
# System of linear equations

2
4
5
g05197
13

Gauss Elimination Method and Applications

Gauss Elimination Method and Applications (to solve linear systems, to find the matrix rank, to find inverse of a matrix)
 
# System of linear equations

3
3
4
g17203
13

Matrix operations

The purpose of this learning graph is, to work with matrix operations. Matrix operation mainly involves three algebraic operations which are addition of matrices, subtraction of matrices, and multiplication of matrices. We can also multiply a matrix by any constants, it is called scalar multiplication.
# Matrices
# Operation

3
5
4
g26196
13

Elementary matrix operations, rank and inverse

Elementary matrix operations play a vital role in applications of algebra. It helps in solving linear equations in finding the inverse of a matrix and also finding the matrix rank. The three basic elementary operations or transformation of a matrix are: - Interchange of any two rows or two columns. - Multiplication of row or column by a non-zero number. - Multiplication of row or column by a non-zero number and add the result to the other row or column.
 
# Matrices

3
7
1
g49195
13

Proportional Relations

A learning graph deals about proportionality and the slope of proportional relations.
# Direct proportionality & rule of three
# Linear functions

4
7
3
p0573
9