## Tutoring on Using The Matrix Equation

Learning Objectives:

#### Understand to Solve Matrix Equations.

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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