Matrices II

Grade 12 · Mathematics

Semester 1 | Period 2 | Week 7

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Subject: Mathematics

Semester: 1

Period: 2

Week: 7

WEEK 7

Class: Grade 12
Age: 17 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Matrices II
Focus: Transpose of a matrix, Determinant of a matrix (2x2) and (3x3), Solution of simultaneous equations using determinant method (two equations in two unknowns and three equations in three unknowns), Inverse of 2x2 matrix.

 

SPECIFIC OBJECTIVES:

By the end of the lesson, students should be able to:

  1. Find the transpose of a matrix by interchanging its rows and columns.
  2. Calculate the determinant of a 2x2 and 3x3 matrix.
  3. Use the determinant method to solve simultaneous equations (two equations in two unknowns and three equations in three unknowns).
  4. Find the inverse of a 2x2 matrix.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Practice exercises
  • Group work
  • Real-life examples

 

INSTRUCTIONAL MATERIALS:

  • Matrix charts
  • Determinant charts
  • Whiteboard and markers
  • Computer with instructional materials

 

 

PERIOD 5: Solution of Simultaneous Equations Using Determinants

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of solving simultaneous equations using determinants.

Students listen and take notes.

Step 2 - Example 1: Two equations in two unknowns

Solves two simultaneous equations using the determinant method. Example: x + 2y = 5, 3x−y=4. The solution is found using Cramer's Rule.

Students observe and understand the process of solving using determinants.

Step 3 - Example 2: Three equations in three unknowns

Solves three simultaneous equations using determinants. Example: x+y+z=6, 2x−y+z=5, x + 2y + 3z = 10.

Students follow and practice solving the system of equations.

NOTE ON BOARD:

  • Cramer's Rule:
    • For two equations:
    • For three equations: Determinants for matrices are used.

EVALUATION (5 exercises):

  1. Solve the system of equations using determinants: x+2y=4, 3x−y=5.
  2. Solve the system of equations: x+y+z=10, 2x - y + z = 8, 3x + 2y + z = 12.
  3. Solve 2x+y=7, x + 3y = 6 using determinants.
  4. Use determinants to solve the system: 2x+3y=10, 4x - y = 5.
  5. Solve x+y=3, 2x + 3y = 8.