Page 105 - ADVANCED MATH F.5

Form Five Form Five

x
 a 11 a 12 a  13 
y , and
d
in the form Ax = where A =   a 21 a 22 a 23   , x = 

 d  1   a 31 a 32 a 33   
z

FOR ONLINE READING ONLY
d =   d 2  
 d 
 3 
−
1
d
2. Guide students to pre-multiply the equation Ax = by A
on both sides:
1
AAx = A d . But AA I= where I is an identity matrix.
1
−
−
1 −
1
−
Assist them to multiply on both sides to obtain, Ix = A d
3. Use Example 5.49 in the Student’s Book to guide students to
find the unknown values of x, y, and z using the inverse matrix
method. Engage students to use scientific calculators or Maple
to verify the answers of the given example.
4. Require students to attempt Exercise 5.8, in the student’s Book.
Advise students to submit their work, check the correctness of
their answers, and provide them constructive feedback.

Answers to Exercise 5.8

 2 10 26 
1
−
1 (a) R = 1  16 − 20 8  (b) x = 1, y = − 2, z = 3
100    
 22 10 − 14 
2. (a) ( , ,x yz ) (3, 1, 4= ) (b) ( , ,x yz ) (3, 2, 1= )

(c) ( , ,x yz ) ( 4.714,= − − 2.071, 5.86− ) (d) ( , ,x yz ) ( 1, 2, 3= − )

(e) ( , ,x yz ) (8, 11, 3= − ) .

 8 8 8 
3. (a) −   7 11 − 1   (b) x = 1, y = − y = 2, z = 3, z = − 32
 
 − 5 1 13 

99
Mathematics for Advanced Secondary Schools

ADVANCED MATH F.5 TG CHAPTERS.indd 99 30/06/2024 18:02:22
ADVANCED MATH F.5 TG CHAPTERS.indd 99
30/06/2024 18:02:22