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: 17
Grade code: 2.1.1.LI.2
Strand code: 1
Sub-strand code: 1
Content standard code: 2.1.1.CS.4
Indicator code: 2.1.1.LI.2
Theme: MODELLING WITH ALGEBRA
Subtheme: APPLICATION OF ALGEBRA
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This lesson introduces the concept of matrix multiplication, a powerful tool used to organise and manipulate large sets of data efficiently. While it may seem abstract, matrix multiplication is the engine behind many real-world applications, from calculating the total cost of items in a market to creating computer graphics for video games and animations. In Ghana, it can help a small business owner calculate their revenue from different products or help a school sports coordinator quickly calculate house points during an inter-house competition. By mastering this skill, you are learning a fundamental concept in higher mathematics and computer science.
Concept 1: The Condition for Matrix Multiplication (Conformability)
Before we can multiply two matrices, we must check if it's even possible. This is called checking for conformability.
The Rule: Two matrices, A and B, can be multiplied in the order AB *only if* the number of columns in the first matrix (A) is equal to the number of rows in the second matrix (B).
Let's represent the order (dimensions) of a matrix as `(rows x columns)`. If Matrix A has order `m x n` and Matrix B has order `p x q`. The product AB is possible only if n = p. Visual Check: Write the orders side-by-side: `(m x n) * (p x q)`. If the two "inner" numbers (`n` and `p`) are the same, you can multiply them. Order of the Resulting Matrix: The resulting matrix, C = AB, will have the order of the "outer" numbers: `m x q`.