5
0
2
6
3
2
x
y
z
a
b
c
−






 = 











, then x = – 1 5, y = 0, z = 2, a = 
6 , b = 3, c = 2
Example 4 If  
3
4
2
7
0
6
3
2
6
1
0
6
3
2
2
3
21
0
2
4
21
0
x
z
y
y
a
c
b
b
+
+
−
−








−
−
= −
−
+








−
−
+
−




Find the values of a, b, c, x, y and z Solution As the given matrices are equal, therefore, their corresponding elements
must be equal Comparing the corresponding elements, we get
x + 3 = 0,
z + 4 = 6,
2y – 7 = 3y – 2
a – 1 = – 3,
0 = 2c + 2
b – 3 = 2b + 4,
Simplifying, we get
a = – 2, b = – 7, c = – 1, x = – 3, y = –5, z = 2
Example 5 Find the values of a, b, c, and d from the following equation:
2
2
4
3
5
4
3
11
24
a
b
a
b
c
d
c
d
+
−
−




=




−
+




Rationalised 2023-24
 42
MATHEMATICS
Solution By equality of two matrices, equating the corresponding elements, we get
2a + b = 4
5c – d = 11
a – 2b = – 3
4c + 3d = 24
Solving these equations, we get
a = 1, b = 2, c = 3 and d = 4
EXERCISE 3