Page 32 - Past Year

30 | P a g e

 3 4 
(b) Given P    . Show that P   7I and P   7P. Hence, find P and P .
2
3
5
4
  4  3 

37. Aini spent RM 11 tp buy 4 pens, 2 rulers and 1 erasers. Nora spent RM9 fot 2 pens, 3 rulers
and 2 erasers. While, Dila spent RM13 for 3 pens, 4 rulers and 3 erasers.
(a) (i) Write the information given above as a system of linear equations in the
form of matrix equation, AX 
B
(ii) Find the cofactor matrix of A and hence determine the determinant of matrix
A

(iii) Determine the adjoint matrix of A and hence find the inverse of A

(b) What is the price of each pen, ruler and eraser?

(c) How much will each person spend if the price of each pen, ruler and eraser increased
by 20%?

 1  1 1  2  3 0 0  1 



1 ,V 
38. Given A   0 1 0 ,S     0 1 0 and U    p




 

p
 1 0 0      0 0 2    1 


2
(a) Compute W  S V .Hence find the value of p such that WU  p .
T
T
VA
(b) Compute   .VA T Hence, show that    A V .
T
T

39. A system of linear equations is given as follows:
2x  3y  4z  11

4x  3y z  10
x  2y  4z  8
(a) Write the above system of linear equation in the form of matrix equation AX  B
where , and are the coefficient matrix, the variable matrix and the constant
matrix respectively. Hence, determine

.
(i) the determinant of A, A
(ii) the matrix od cofactor , and

(iii) the adjoint matrix A, ( ).