Page 104 - ADVANCED MATH F.5

Form Five Form Five

Adjoint and Inverse of a 33× matrix
Teaching steps
1. Guide students in groups to discuss the concept of adjoint of a
matrix A as the transpose of the matrix of cofactors of matrix
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A. Design learning activities that will help students to generate
the elements of the adjoint of matrix using the formula:
Adj A = ) T ( ij+ M ) .
( ) (cof(A) , where cof(A)= ( 1)−
ij
2. Assist students to discuss the inverse of a 33× matrix. Guide
students to discuss properties of the inverse of a matrix as
stipulated in the Student’s Book. Ask students to search for
more properties of the inverse of the 33× matrix from the
suggested resources.

3. Guide students to discuss the inverse of a 33× of a matrix
Adj(A)
1
A using the formula A = where Adj(A) is the
−
abbreviation for adjoint. A
4. Use Example 5.48 in the Student’s Book to guide students to
find the inverse of a matrix by finding determinant, minors,
cofactors, and adjoint of a given matrix. Engage students to
use a scientific calculator or Maple to verify the inverse of a
matrix from the given example. Advise students to share their
work with other groups for more iputs.

Solution of systems of linear equations using inverse matrix
method or determinant method
Teaching steps

1. Guide students in groups to consider the 33× system of linear
simultaneous equations of the form:
x
 a 11 a 12 a    d 
13
1
 a a a    d  . Lead them to write the system
y =
 21 22 23    2 
    
z
 a 31 a 32 a 33    d 3 
98
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:21
ADVANCED MATH F.5 TG CHAPTERS.indd 98
ADVANCED MATH F.5 TG CHAPTERS.indd 98 30/06/2024 18:02:21