SHS2 Additional Mathematics · Semester 1 Week 15: Application of Algebra

Lesson notes

Learning Objectives

Indicator: 2.1.1.LI.2 - Multiply an m x n matrix by an n x 1 matrix.

By the end of the lesson, learners can:

State the condition for two matrices A (m x n) and B (n x 1) to be conformable for the product AB.
Multiply an m x n matrix by an n x 1 matrix correctly, showing each step of the row-by-column process.
Determine whether the product of two given matrices exists and, when it does not, explain why in terms of the dimensions.
Apply multiplication of an m x n matrix by an n x 1 matrix to solve a practical problem involving weighted totals or allocations.
Justify, using a counterexample, that matrix multiplication is not commutative, that is, AB is not always equal to BA.

Sign in with your phone number to read the full note and download the GES plan - free.

Sign in with phone number

Curriculum details

Strand: Modelling with Algebra (Strand 1)
Sub-strand: Application of Algebra (1.1)
Content standard: 2.1.1.CS.4 - Demonstrate the ability to carry out matrix operations, determine the inverse of a linear transformation and represent real life situations in matrix forms. 2.1.1.LO.1 Investigate De Morgan's law on sets algebraically and graphically, formulate and solve real life problems up to three sets. 2.1.1.LO.2 Model sequence recursively and explicitly, and establish the relationship between the two forms, as well as solve real life problems involving linear and exponential sequences and series. 2.1.1.LO.3 Apply indices and logarithms to solve real life problems, including logarithms with different bases, and sketch and interpret logarithmic functions. 2.1.1.LO.4 Formulate and derive appropriate strategies to solve quadratic inequalities. 2.1.1.LO.5 Graph systems of given inequality and identify the region that provides the feasible solution and apply it to real life situations. 2.1.1.LO.6 Determine the set of values for which a rational function is defined and resolve rational functions into partial fractions. 2.1.1.LO.7 Multiply matrices, determine the inverse of a 2 x 2 matrix, find the determinant up to a 3 x 3 matrix and represent matrices in linear transformations.
Indicator: 2.1.1.LI.2 - Multiply an m x n matrix by an n x 1 matrix. Collaborative Learning, Experiential Learning, Problem-based Learning, Project-based Learning and Talk for Learning
Suggested placement: Semester 1, Week 15 (Week 15 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

exemplars - p.321: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
Curriculum reference: NaCCA curriculum document, p. 321

Exemplars (from the NaCCA curriculum)

Activity: Exploring the possibilities of multiplying given matrices.
Collaborative Learning, Experiential Learning, Whole class discussion, Talk for Learning Approaches and Problem-based Learning.
Work with a partner: Learners explore matrix multiplication, multiplying 𝑚 × 𝑛 matrix by an 𝑛 × 1 matrix. Learners recognise that two matrices, A and B, are said to be confirmable for product AB if the number of columns in A equals the number of rows in matrix B.
Example: 1 2 2 3 −5 Let 𝐴 = Ÿ −3 0 and 𝐵 = i j 0 6 −2 −5 −1 Calculate (i) AB (ii) BA (iii) is AB = BA?
Teaching and Learning Resources:
- Worksheets
- Scientific Calculator
- Technological tools, apps, etc.
Assessment (2.1.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 4 Extended critical thinking and reasoning.