4.0 MATRICES AND SYSTEMS OF LINEAR EQUATIONS
Question 1
3 1 1 


2
Given A  1 3 1 . Find the values m and n such that A  mA  nI  0 where
1 1 3
identity matrix and 0 is zero matrix. Use this relation to obtain A1 and show that
I is
3 3
A3  39 A  70 I .
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Question 2
:
If B =
 2 4 3 
 1 2 1

 . Find B – 1 using ERO.
 2 3 1 
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Question 3
:
1 3 9 


Given A = 5 1 3  B =
1 3 7 
 1 3 0
 2 1 3 


 1 0 1 
Find AB and A-1. Hence, solve the following linear equations.
x  5y  z  7
3x  y  3z  5
9 x  3 y  7 z  1
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Question 4
:
 1 1 2
 0 2 2
Given A = 
.
 1 1 3
Find A2 – 6A + 11I, with I as an identity matrix 3 x 3. Show that A(A2 – 6A + 11I) = 6 I, hence deduce A-1.
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Question 5
:
Ali, Bob and Ravi bought tickets for three separate performances. The table below shows the number of tickets
bought by each of them.
concert
orchestral
opera
Ali
2
1
1
Bob
1
1
1
Ravi
2
2
1
(a)
(b)
(c)
If the total cost for Ali was RM 122, for Bob RM 87 and for Ravi RM 146, represent this information in
the form of three equations.
Find the cost per ticket for each of the performances using G-J elimination method.
Determine how much it would cost Hassan to purchase 2 concerts, 1 orchestral and 3 opera tickets.
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Question 6
:
Hassan came out of the post office after spending RM12.00 on 20 cent,30 cent and 50cent stamps. He bought 40
stamps altogether and the amount of 20 cent bought is equal to the sum of the amount of 30 cent stamps and 50
cent stamps bought.
a)
Write 3 linear equations to represent the above information. Hence transform the linear equations to a
matrix equation of the form of AX = B.
b)
By using the Gauss-Jordan Elimination method, find how many of each type of stamps that Hassan has
bought.
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