Scroll:matrices >> find the value >> ps (4141)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.


 

1)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
22
23
 		, B = 
2-2
24
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




2)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
52
24
 		, B = 
4-2
53
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




3)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
32
31
 		, B = 
1-2
45
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




4)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
12
33
 		, B = 
1-2
45
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




5)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
62
21
 		, B = 
3-2
24
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




6)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
32
23
 		, B = 
3-2
31
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




7)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
62
41
 		, B = 
3-2
23
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




8)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
42
22
 		, B = 
3-2
31
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




9)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
42
45
 		, B = 
3-2
23
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




10)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
62
31
 		, B = 
4-2
21
 		and O = 
00
00
 

(i)  A+B =  

(ii)  A+(-A) = O

 


Answer:_______________




 

1)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
22
23
 		, B = 
2-2
24
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
22
23
 		, B = 
2-2
24
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
2 2
2 3
+
2-2
24
= 
40
47
 		....(1)
B+A
2 -2
2 4
+
22
23
= 
40
47
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
22
23
 +
-2-2
-2-3
= 
00
00
= O ...(3)
(-A) + A
-2-2
-2-3
 +

 

22
23

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



2)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
52
24
 		, B = 
4-2
53
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
52
24
 		, B = 
4-2
53
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
5 2
2 4
+
4-2
53
= 
90
77
 		....(1)
B+A
4 -2
5 3
+
52
24
= 
90
77
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
52
24
 +
-5-2
-2-4
= 
00
00
= O ...(3)
(-A) + A
-5-2
-2-4
 +

 

52
24

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



3)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
32
31
 		, B = 
1-2
45
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
32
31
 		, B = 
1-2
45
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
3 2
3 1
+
1-2
45
= 
40
76
 		....(1)
B+A
1 -2
4 5
+
32
31
= 
40
76
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
32
31
 +
-3-2
-3-1
= 
00
00
= O ...(3)
(-A) + A
-3-2
-3-1
 +

 

32
31

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



4)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
12
33
 		, B = 
1-2
45
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
12
33
 		, B = 
1-2
45
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
1 2
3 3
+
1-2
45
= 
20
78
 		....(1)
B+A
1 -2
4 5
+
12
33
= 
20
78
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
12
33
 +
-1-2
-3-3
= 
00
00
= O ...(3)
(-A) + A
-1-2
-3-3
 +

 

12
33

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



5)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
62
21
 		, B = 
3-2
24
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
62
21
 		, B = 
3-2
24
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
6 2
2 1
+
3-2
24
= 
90
45
 		....(1)
B+A
3 -2
2 4
+
62
21
= 
90
45
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
62
21
 +
-6-2
-2-1
= 
00
00
= O ...(3)
(-A) + A
-6-2
-2-1
 +

 

62
21

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



6)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
32
23
 		, B = 
3-2
31
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
32
23
 		, B = 
3-2
31
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
3 2
2 3
+
3-2
31
= 
60
54
 		....(1)
B+A
3 -2
3 1
+
32
23
= 
60
54
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
32
23
 +
-3-2
-2-3
= 
00
00
= O ...(3)
(-A) + A
-3-2
-2-3
 +

 

32
23

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



7)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
62
41
 		, B = 
3-2
23
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
62
41
 		, B = 
3-2
23
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
6 2
4 1
+
3-2
23
= 
90
64
 		....(1)
B+A
3 -2
2 3
+
62
41
= 
90
64
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
62
41
 +
-6-2
-4-1
= 
00
00
= O ...(3)
(-A) + A
-6-2
-4-1
 +

 

62
41

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



8)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
42
22
 		, B = 
3-2
31
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
42
22
 		, B = 
3-2
31
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
4 2
2 2
+
3-2
31
= 
70
53
 		....(1)
B+A
3 -2
3 1
+
42
22
= 
70
53
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
42
22
 +
-4-2
-2-2
= 
00
00
= O ...(3)
(-A) + A
-4-2
-2-2
 +

 

42
22

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



9)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
42
45
 		, B = 
3-2
23
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
42
45
 		, B = 
3-2
23
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
4 2
4 5
+
3-2
23
= 
70
68
 		....(1)
B+A
3 -2
2 3
+
42
45
= 
70
68
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
42
45
 +
-4-2
-4-5
= 
00
00
= O ...(3)
(-A) + A
-4-2
-4-5
 +

 

42
45

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A

 

 

 



10)  

 Verify (i)  A+B =B+A   (ii)  A+(-A) = O = (-A)+A.


If A = 
62
31
 		, B = 
4-2
21
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
62
31
 		, B = 
4-2
21
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
6 2
3 1
+
4-2
21
= 
100
52
 		....(1)
B+A
4 -2
2 1
+
62
31
= 
100
52
 		....(2)

 From (1) and (2)

A+B = B+A.

(ii) To prove A+(-A) = O = (-A)+A

A+ (-A)
62
31
 +
-6-2
-3-1
= 
00
00
= O ...(3)
(-A) + A
-6-2
-3-1
 +

 

62
31

 

= 
00
00
 		= O...(4)

From (3) and (4) 

A+(-A) = O = (-A)+A