System of Linear Equations Solution

Understand how to solve systems of linear equations by applying matrix algebra techniques including matrix inversion and Gaussian elimination. Learn to implement these methods in R and C++ using libraries like RcppArmadillo and Eigen for efficient computation. This lesson equips you with practical skills to compute solutions and verify results across different matrix algebra tools.

We'll cover the following...

System of linear equations
The solve() function in R
Gaussian elimination algorithm
Solve with Armadillo
Solve with Eigen

System of linear equations

A system of linear equations takes the following form:

𝐴𝑥 = 𝑏

In this equation:

$𝐴$ is a square coefficient matrix.
$𝑥$ is the vector of unknowns.
$𝑏$ is the RHS (right hand side) vector.

It can be solved by multiplying the inverse of matrix $𝐴$ by RHS constant vector $𝑏$ :

𝑥 = 𝐴^{−1}𝑏

Let’s suppose, the system of linear equations is formed by two equations and two unknowns:

\begin{aligned} x_{1} - 1 * x_{2} = 2 \end{aligned}

1.Introduction

2.Assignment Operator

3.Addition of Matrices

4.Scalar Multiplication of Matrices

5.Multiplication of Matrices

6.Transposition of Matrices

7.Determinant of a Matrix

8.Inverse of a Matrix

9.System of Linear Equations

Project

10.LU Matrix Factorization

11.Cholesky Factorization

12.QR Matrix Factorization

13.Eigendecomposition

14.Wrapping It Up

System of Linear Equations Solution

System of linear equations