Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Represent systems of linear equations using matrices.
• Solve systems of linear equations using matrix methods.
• Apply matrices to solve real-life problems.

Lesson summary

In our daily lives, we often face situations with multiple unknown quantities and several related conditions. For example, a market woman trying to determine the price of individual items based on bulk sales, or an engineer calculating different forces acting on a structure. While we can use traditional methods like substitution or elimination to solve these simultaneous equations, these methods can become very cumbersome for complex problems. This lesson introduces a powerful and systematic tool from algebra: matrices. We will learn how to represent real-life problems as matrix equations and solve them efficiently.

Lesson notes

Part 1: Representing Simultaneous Equations in Matrix Form

Any system of linear equations can be written in the form AX = B, where: A is the Coefficient Matrix (the numbers in front of the variables). X is the Variable Matrix (the unknown variables, written as a column). B is the Constant Matrix (the numbers on the right-hand side of the equals sign, written as a column).

Example (2x2 system): Consider the system: 2x + 3y = 13 5x + 2y = 16

In matrix form, this becomes: $$ \begin{pmatrix} 2 & 3 \\ 5 & 2 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 13 \\ 16 \end{pmatrix} $$ Where: A = $ \begin{pmatrix} 2 & 3 \\ 5 & 2 \end{pmatrix} $ X = $ \begin{pmatrix} x \\ y \end{pmatrix} $ B = $ \begin{pmatrix} 13 \\ 16 \end{pmatrix} $

Evaluation guide

• Model and solve problems based on real life situations using matrices.
• Collaborative Learning, Experiential Learning, Problem -based Learning, Project -based
• Learning and Talk for Learning
• Activity: Application of Matrices to Simultaneous Equations