Applications of Algebra

Curriculum details

Strand

Modelling with Algebra (Strand 1)

Sub-strand

Applications of Algebra (1.2)

Content standard

3.1.2.CS.2 - Demonstrate the ability to use and apply knowledge of matrices in linear transformations and apply a linear transformation to solve problems in context. 3.1.2.LO.1 Construct compound statements and truth tables using connectives. 3.1.2.LO.2 Apply linear transformation in: finding images of points and object points. finding reflections and rotations of points and plane figures.

Indicator

3.1.2.LI.3 - Find the composition of linear transformations.

Suggested placement

Semester 1, Week 6 (Week 6 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.455: 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. 455

Exemplars (from the NaCCA curriculum)

Think-pair-share, Talk for Learning, and Building on what others say.
Learning Experience: Learners in convenient groups discuss and determine the composition of linear transformations.
Activity 1: Composition of linear transformations This occurs when an object undergoes two or more transformations, one after the other. Thus, 𝐴(𝑥, 𝑦 ). 𝐵(𝑥, 𝑦 ) is defined as the transformation the matrix 𝐵, followed by the transformation of matrix 𝐴. This is calculated as follows:
- Write the matrix 𝐴 and 𝐵 of the linear transformation.
- Find the matrix product 𝐴.
- Write the linear transformation for 𝐴. That is 𝐴(𝑥, 𝑦 ).
- Notice that the matrix that represents the first transformation, A, is placed on the right, and the second transformation, B, is placed on the left in the matrix product.
2 −3 1 3 Example 1: Given the matrices 𝐴 = É Ê and 𝐵 = É Ê, find the matrix of the transformation 5 7 −1 4 𝐴, followed by 𝐵. 

2 1 −1 2 Example 2: Given that 𝑀 = É Ê and 𝑁 = É Ê, find the image of the point (2, 3) under the 2 3 4 1 transformation 𝑀 ○ 𝑁. 

Example 3: Let𝑆: (𝑥, 𝑦) → (−𝑥, 𝑦) and 𝑇(𝑥, 𝑦) → (−𝑦, 𝑥) be two linear transformations in the 𝑥- 𝑦 plane. Find a single matrix representing the composite transformation TS.

Example 4: Two linear transformations are defined by: 𝐴(𝑥, 𝑦) → (2𝑥- 𝑦, 3𝑥 + 2𝑦) and 𝐵(𝑥, 𝑦) → (3𝑥 + 2𝑦, 4𝑦) Find the matrix representing 𝐴 ○ 𝐵. 

Teaching and Learning Resources:
- SHS Curriculum, Graph boards, mathematical set, ICT tools
Assessment (3.1.2.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.