1
ENGINEERING MATHEMATICS 1A (MAT 1058)
WORKSHEET#6
Matrix and Determinant
1.
 1 2
Given that A = 
,
 −1 3
Find the following:
(i) BT
(ii) 3 A − 2C
(iii)
CA
 0 − 2 3
B=
,
 −1 3 1 
0
 1
 −5 2 

C=
, D = −1
4 


 1 −7 
 2 − 3 
2
(iv) DB
(v)
C −1
3
(vi)
2.
AT B
Find:
 −2 x − y 
i) −3 y 

 − 4 y −3 x 
4
ii)
 x + y   −5 
 x − 6  +  −6 xy 

 

 −5u −v 
iii)  2 −5v  
6 
 0
5
3.
Solve the following for unknowns:
i)
 4x
17   −24 17 

=

 y + 2 −42   15 −42 
ii)
4  5 y
6   −10 10 
3 x + 5
+
=
 7

x − 1  7 3 y + 1  14 −9 

6
iii)
 −4 − y   −4 x 0   −16 5 
 −2 x −4   0 −5 =  8 x 2 20 


 

7
4.
Show that the following are singular matrices:
8 6 
3
(i)

2 2 
A matrix A is singular if the determinant
of A is zero.
2 − 1 5
(ii) 4 3 1


2 − 1 5
8
5.
 t − 11
Given that M = 
 . If M
4 − 9 
6.
Find the inverse of the following matrices
i)
 1 2
A=

 −1 3
80 , find the value of t.
9
 −5 2 
ii) C = 

 1 −7 
10
7.
Solve the following using matrix inverse method.
i)
3x − y = 5
2x + y = 5
11
ii)
x −y =5
2x − y = 6
12
iii)
2x − 2 y = 3
7 x − 8 y = −2
13
 5 −2 
 16 
iv) 
X = 
7 6 
 −4 
14
8.
Use Cramer’s rule to solve for the following unknowns:
i)
x −y =5
2x − y = 6
15
ii)
− x + y + 2z = 7
2x + 3y + z = 1
− 3x − 4 y + z = 4
16
iii)
x + y + z = −5
x − 4 y + z = 35
x + 3 y + 4 z = −18
.
17
iv)
x + y + z=0
2 x + y = 2 z − 8 (solve for y only)
− x + 4 z = 10
18
19
9.
Cory, Josh and Dan went shopping for Halloween treats. Cory bought 3 chocolate
pumpkins, 4 masks and 8 candy witches. He spent $36.65. Josh bought 5 chocolate pumpkins,
3 masks and 10 candy witches. He spent $37.50. Dan bought 4 chocolate pumpkins, 5 masks
and 6 candy witches. He spent $43.45. Write a system of equations to represent this problem
and algebraically calculate the unit price of each item purchased.
Final Answer:
Each chocolate pumpkin costs $2.55.
Each mask costs $5.75.
Each candy witch costs $.75.