JIM 201 2018 2019 Assignment 1

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PUSAT PENGAJIAN PENDIDIKAN JARAK JAUH
UNIVERSITI SAINS MALAYSIA
ACADEMIC SESSION 2018/2019
JIM 201 – LINEAR ALGEBRA
Assignment 1 : 10 %
Course Manager: Assoc. Prof. Mohd. Nain Hj. Awang
ANSWER ALL QUESTIONS.
Due date: 30th December 2018
1.
4 − 2
 5

Given that matrix A =  4
5 − 2  such that A2 +  A +  I = O
 −2 − 2
2 
where I is an identity matrix 3  3 and O is a zero matrix 3  3.
Determine the values of  and  .
 2 −1
2
2. Given that matrix B =  3
 −1
0
k 
4 
k + 2 
and
B = 27 .
Find the value of
(b) BT B 2
(a) k , where k is an integer
(c ) B T B 3 B T
3 Using only elementary row operations and theorems, show that
1 a
1 b
1 c
bc
ca = ( a − b )( b − c )( c − a )
ab
3 −1   1 −1
 3

1   0
2
4. Find  −2 − 2
 −4 − 5
2   2
3
1 
− 1  . Hence, solve the system
0 
3x + 3 y − z = 2
− 2 x − 2 y + z = −1
− 4x − 5 y + 2z = 0
5. Solve the system of equations
5 x − 3 y + 2 z = 13
− 2 x + y + 3z = −1
2x − y + 2z = 6
by using
(a)
the inverse method
(b)
the Gauss-Jordan elimination method
(c)
Cramer’s Rule
1 2
6. (a) Find the inverse matrix of C =  2 4
 3 5
3
5  .
6 
(b) The table below shows the number of boxes of milk P , Q and R which were
supplied by a dairy to three houses in a village every week.
House/Milk
Milk P
Milk Q
Milk R
1st House
1
2
3
2nd House
2
4
5
3 rd House
3
5
6
The payment collected by the dairy owner from the first, second and third houses are
RM130, RM 235 and RM 295 respectively. If x, y and z are the prices for each box of
the milk, write a system of linear equation from the above information. Then,
determine the values of x, y and z using inverse matrix.
000000000000000
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