Lesson Notes By Weeks and Term v4 - SHS 2
APPLICATION OF ALGEBRA
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APPLICATION OF ALGEBRA
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Subject: Additional Mathematics
Class: SHS 2
Term: 1st Term
Week: 18
Grade code: 2.1.1.LI.4
Strand code: 1
Sub-strand code: 1
Content standard code: 2.1.1.CS.4
Indicator code: 2.1.1.LI.4
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATION OF ALGEBRA
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Algebra is more than just solving for *x* and *y*; it is a powerful language for describing and solving real-world problems. In our communities, from the market woman calculating her daily sales to the engineer designing a new road, people constantly face situations with multiple unknown quantities and conditions. This lesson introduces a highly organized method for handling such problems: using matrices. We will learn how to translate complex situations, described in words or as equations, into a compact matrix format (`AX = B`). This skill is the foundation for solving large systems of equations efficiently, which has applications in economics, computing, science, and business.
Part 1: From Simultaneous Equations to Matrix Form
A system of simultaneous linear equations is a set of two or more linear equations with the same variables. For example: `2x + 3y = 13` `5x + 2y = 16`
Our goal is to represent this system in the matrix form `AX = B`. Let's break down what each part means: A - The Coefficient Matrix: This is a matrix formed by the coefficients (the numbers multiplying the variables) of the equations. The coefficients must be taken in the order they appear. X - The Variable Matrix: This is a single-column matrix containing the variables (`x`, `y`, `z`, etc.). B - The Constant Matrix: This is a single-column matrix containing the constant terms (the numbers on the right side of the equals sign).
How to Assemble the `AX = B` Form