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 = 
62
45
 		, B = 
2-2
25
 		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
44
 		, B = 
4-2
54
 		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 = 
52
25
 		, B = 
4-2
25
 		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
45
 		, B = 
3-2
32
 		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 = 
52
32
 		, B = 
1-2
23
 		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 = 
22
45
 		, B = 
4-2
54
 		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 = 
22
32
 		, B = 
3-2
34
 		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 = 
12
21
 		, B = 
4-2
44
 		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 = 
62
25
 		, B = 
4-2
43
 		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 = 
22
24
 		, B = 
2-2
42
 		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 = 
62
45
 		, B = 
2-2
25
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
62
45
 		, B = 
2-2
25
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
6 2
4 5
+
2-2
25
= 
80
610
 		....(1)
B+A
2 -2
2 5
+
62
45
= 
80
610
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
62
45
 +
-6-2
-4-5
= 
00
00
= O ...(3)
(-A) + A
-6-2
-4-5
 +

 

62
45

 

= 
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
44
 		, B = 
4-2
54
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
52
44
 		, B = 
4-2
54
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
5 2
4 4
+
4-2
54
= 
90
98
 		....(1)
B+A
4 -2
5 4
+
52
44
= 
90
98
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
52
44
 +
-5-2
-4-4
= 
00
00
= O ...(3)
(-A) + A
-5-2
-4-4
 +

 

52
44

 

= 
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 = 
52
25
 		, B = 
4-2
25
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
52
25
 		, B = 
4-2
25
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
5 2
2 5
+
4-2
25
= 
90
410
 		....(1)
B+A
4 -2
2 5
+
52
25
= 
90
410
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
52
25
 +
-5-2
-2-5
= 
00
00
= O ...(3)
(-A) + A
-5-2
-2-5
 +

 

52
25

 

= 
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
45
 		, B = 
3-2
32
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
12
45
 		, B = 
3-2
32
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
1 2
4 5
+
3-2
32
= 
40
77
 		....(1)
B+A
3 -2
3 2
+
12
45
= 
40
77
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
12
45
 +
-1-2
-4-5
= 
00
00
= O ...(3)
(-A) + A
-1-2
-4-5
 +

 

12
45

 

= 
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 = 
52
32
 		, B = 
1-2
23
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
52
32
 		, B = 
1-2
23
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
5 2
3 2
+
1-2
23
= 
60
55
 		....(1)
B+A
1 -2
2 3
+
52
32
= 
60
55
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
52
32
 +
-5-2
-3-2
= 
00
00
= O ...(3)
(-A) + A
-5-2
-3-2
 +

 

52
32

 

= 
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 = 
22
45
 		, B = 
4-2
54
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
22
45
 		, B = 
4-2
54
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
2 2
4 5
+
4-2
54
= 
60
99
 		....(1)
B+A
4 -2
5 4
+
22
45
= 
60
99
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
22
45
 +
-2-2
-4-5
= 
00
00
= O ...(3)
(-A) + A
-2-2
-4-5
 +

 

22
45

 

= 
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 = 
22
32
 		, B = 
3-2
34
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
22
32
 		, B = 
3-2
34
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
2 2
3 2
+
3-2
34
= 
50
66
 		....(1)
B+A
3 -2
3 4
+
22
32
= 
50
66
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
22
32
 +
-2-2
-3-2
= 
00
00
= O ...(3)
(-A) + A
-2-2
-3-2
 +

 

22
32

 

= 
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 = 
12
21
 		, B = 
4-2
44
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
12
21
 		, B = 
4-2
44
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
1 2
2 1
+
4-2
44
= 
50
65
 		....(1)
B+A
4 -2
4 4
+
12
21
= 
50
65
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
12
21
 +
-1-2
-2-1
= 
00
00
= O ...(3)
(-A) + A
-1-2
-2-1
 +

 

12
21

 

= 
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 = 
62
25
 		, B = 
4-2
43
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
62
25
 		, B = 
4-2
43
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
6 2
2 5
+
4-2
43
= 
100
68
 		....(1)
B+A
4 -2
4 3
+
62
25
= 
100
68
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
62
25
 +
-6-2
-2-5
= 
00
00
= O ...(3)
(-A) + A
-6-2
-2-5
 +

 

62
25

 

= 
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 = 
22
24
 		, B = 
2-2
42
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
22
24
 		, B = 
2-2
42
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
2 2
2 4
+
2-2
42
= 
40
66
 		....(1)
B+A
2 -2
4 2
+
22
24
= 
40
66
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
22
24
 +
-2-2
-2-4
= 
00
00
= O ...(3)
(-A) + A
-2-2
-2-4
 +

 

22
24

 

= 
00
00
 		= O...(4)

From (3) and (4) 

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