Learning Objectives:

__Math Tutoring on Using The Matrix Equation__

A system of equations can also be solved by **Matrix Method.** This Matrix Method of solving systems of equations involves expressing the system of equations in the form of a matrix and then reducing that matrix in Row Echelon Form. **The Matrix Equation:**

**AX = B**

**A-1AX = A-1B**

**InX = A-1B **

**X = A-1B**

We can solve the system using **LU Decomposition,** where **L** is a **lower triangular matrix** and **U** is an **upper triangular matrix.**

Let **A = LU** and substitute into **AX = B.**

We have to now solve **LUX = B** for **X** to solve the system.

Let **UX = Y,**

then, **LY = B** and **UX = Y**

Now we first solve **LY = B** for **Y** and then solve **UX = Y** for **X.**

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**Hook Questions:**

*1. **What is the use of Matrix Equations in solving a System of Two Equations?*

*2. **What is LU Decomposition?*

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