Lesson Notes By Weeks and Term v4 - SHS 3
APPLICATIONS OF ALGEBRA
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
APPLICATIONS OF ALGEBRA
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
Subject: Additional Mathematics
Class: SHS 3
Term: 1st Term
Week: 10
Grade code: 3.1.2.LI.3
Strand code: 1
Sub-strand code: 2
Content standard code: 3.1.2.CS.2
Indicator code: 3.1.2.LI.3
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATIONS OF ALGEBRA
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
This lesson explores how we can combine multiple geometric changes, known as linear transformations, into a single, more efficient operation using the power of algebra, specifically matrix multiplication. Think about creating an animation or a video game. A character might need to rotate and then move forward. Instead of telling the computer to do two separate calculations, we can combine them into one. This is the essence of composite transformations. In Ghana, this mathematics is the secret behind digital art, including the creation and manipulation of Adinkra symbols in software, and is fundamental to fields like engineering, architecture, and computer graphics.
This topic builds on your knowledge of matrix multiplication. We will see how matrices are not just for solving simultaneous equations, but are powerful tools for describing geometric movements. A. What is a Linear Transformation?
A linear transformation is a function that maps points from one position in a plane to another in a structured way. It preserves straight lines (a line transforms into another line) and the origin remains fixed. We can write a transformation `T` that moves a point `(x, y)` to a new point `(x', y')` as: `T(x, y) = (x', y')`
For example, a reflection in the x-axis takes a point `(x, y)` to `(x, -y)`. We would write this as: `T(x, y) = (x, -y)` B. Representing Transformations with 2x2 Matrices
Every linear transformation in a 2D plane can be represented by a 2x2 matrix. If a transformation `T` is represented by the matrix `M = [[a, b], [c, d]]`, it maps the point `(x, y)` to `(x', y')` using matrix multiplication: