NORTHERN TECHNICAL COLLEGE
YEAR: February 2021
TERM: 1
CLASS: D8/1
SUBJECT: Engineering Mathematics I / Assignment I.
PROGRAMME: Electrical Engineering Diploma.
1.
 1 2 1
 1 3 4 


Given the matrices A  
 , B   1 5 2  ,

2
1
3


 3 4 3


 1 1 


C   2 2 
 3 3 


Find the following, if possible; (i) A  C (ii) BT  C (iii) BC (iv) AT BT (v) BT AT
2.
An electrical chain has three shops, A, B and C. The average daily sales and profit in
each shop is given in the following table:
Units Sold
Units Profit
Shop A
Shop B
Shop C
Shop A
Shop B
Shop C
Diodes
Resistors
900
600
700
1500
2500
3000
2000
800
900
3500
2500
4000
Capacitors
700
1400
2000
2500
3500
2500
Use matrix multiplication to determine
a) The profit for each product;
b) The profit for each shop
4 7
 1 6 2 
 0 1 12 
 7






3. Given that A   2 3 1  , B   3 4 5  , C   13 1 6 
 1 2 3 
 6 3 7 
 9 8 5 






Find (i) 2 A  3C (ii) 7BC (iii) 7CB (iv) C  2B
(v) det( AB)
(vi) ( AB) 1
ENGINEERING MATHEMATICS I – DIPLOMA IN ELECTRICAL ENGINEERING LEVEL I
4. Find the value of x
if
i)
x2
x
1
x
2
0
ii)
x2
x
2
5
 4
 x2
5. Find the value(s) of k for each of the following;
i)
x y
x
y
y
x y
x
x y
x
y
k
1
1
2
2
3 0
iii)
 k x  y
3
3

ii)
x
y
y
y
x
y   x  2ky  x  ky 
y
y
x
2
1 1 k
 2 3   p

 1 4   r
2q   1 0 

 find the values of p , q , r and s .
s  0 1
6. i) If 
 4
 2
Matrices A and B are defined as A  
ii)
if
.
p
 x 6 
 and B  
 . Find the value of p and x
1
1 3 
B  3 AT
 cos 
  sin 
iii) If A  
sin  
 cos 2
2
 show that A  
cos  
  sin 2
7. Find the values of x if
5 x
7
5
0
4 x
1
2
8
3  x
sin 2 

cos 2 
0
8. A d.c circuit comprises three closed loops. Applying Kirchhoff’s law to the closed loops gives the
following equations for current flow in milliamperes.
 I1  4I3    I1  3I 2   26  0
8I1  I3    4I1  2I3    3I1  5I 2   87  0
3I1  2  3I1  I 2   2  I1  3I 3   12
Use Cramer’s rule to solve for I1 , I 2 and I 3 .
9. Solve the following system by using both Cramer’s rule and inverse method.
2 x  y  z  0,
a)
4 x  3 y  2 z  2,
2 x  y  3z  0.
ENGINEERING MATHEMATICS I – DIPLOMA IN ELECTRICAL ENGINEERING LEVEL I
b)
 P1  2P2    P1  6P2  P3   77  0 ,
 3P3  2P1    P2  2P1   2  P2  2P3   114 ,
 2P2  P1    P2  P1   3P3  48  0
4 x1  x 2  3 x3  8
c)
 2 x1  5 x 2  x3  4
3 x1  2 x 2  4 x3  9
x  3 y  3z  7,
2 x  y  z  4,
d)
x  y  z  4.
4u  3v  2w  5 , 5v  w  11 and 3w  12
e)
ENGINEERING MATHEMATICS I – DIPLOMA IN ELECTRICAL ENGINEERING LEVEL I