Examples for Practice (1.3)
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1. Find the values of the following determinants:
1.
|
4
3
2
1
|
Answer:
− 2
1 Mark
2.
|
1
2
3
4
|
Answer:
− 2
1 Mark
3.
|
1
3
2
4
|
Answer:
− 2
1 Mark
4.
|
1
2
4
3
|
Answer:
− 5
1 Mark
5.
|
2
2
2
2
|
Answer:
0
1 Mark
6.
|
a
b
b
a
|
Answer:
a
2
−
b
2
1 Mark
7.
|
a
b
c
d
|
Answer:
ad
−
bc
1 Mark
8.
|
8
4
5
-
2
|
Answer:
− 36
1 Mark
9.
|
10
2
11
-
1
|
Answer:
− 32
1 Mark
10.
|
2
3
3
2
2
3
3
2
|
Answer:
0
2 Marks
11.
|
2
3
9
-
2
3
3
|
Answer:
36
2 Marks
12. \begin{vmatrix} 3\sqrt{6} & -4\sqrt{2} \\ 5\sqrt{3} & 2 \end{vmatrix}
Answer:
2
2 Marks
13. \begin{vmatrix} \dfrac{7}{3} & \dfrac{5}{3} \\ \dfrac{3}{2} & \dfrac{1}{2} \end{vmatrix}
Answer:
-
4
3
2 Marks
March 20
2. Solve the following equations using Cramer’s Rule:
1.
4
x
− 3
y
= 11
6
x
+ 5
y
= 7
Answer:
x
= 2,
y
= − 1
3 Marks
2.
3
x
+ 5
y
= − 7
x
+ 4
y
= − 14
Answer:
x
= 6,
y
= − 5
3 Marks
3.
x
− 4
y
= − 9
−
x
+ 5
y
= 11
Answer:
x
= − 1,
y
= 2
3 Marks
4.
− 2
x
+ 3
y
= − 3
3
x
− 4
y
= 5
Answer:
x
= 3,
y
= 1
3 Marks
5.
5
x
+
y
= − 13
3
x
− 2
y
= 0
Answer:
x
= − 2,
y
= − 3
3 Marks
6.
2
x
+ 3
y
= 4
x
+
y
= 1
Answer:
x
= − 1,
y
= 2
3 Marks
7.
− 2
x
+ 4
y
= 1
− 2
x
+
y
= − 3
Answer:
x
=
13
6
,
y
=
4
3
4 Marks
8.
3
x
− 2
y
= 3
x
+ 5
y
= 2
Answer:
x
=
19
17
,
y
=
3
17
4 Marks
9.
− 6
x
+
y
= 1
5
x
−
y
= 1
Answer:
x
= − 2,
y
= − 11
3 Marks
10.
x
+ 2
y
= 3
4
x
+ 5
y
= 6
Answer:
x
= − 1,
y
= 2
3 Marks
11.
− 4
x
+ 3
y
= − 4
− 8
x
+ 5
y
= 0
Answer:
x
= − 5,
y
= − 8
3 Marks
12.
3
x
−
y
= 7
x
+ 4
y
= 11
Answer:
x
= 3,
y
= 2
3 Marks
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This page was last modified on
11 March 2021 at 17:05