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 = 
12
33
 		, B = 
3-2
21
 		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 = 
62
43
 		, B = 
1-2
22
 		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 = 
12
33
 		, B = 
1-2
33
 		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 = 
42
41
 		, B = 
3-2
34
 		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 = 
22
34
 		, B = 
4-2
35
 		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
33
 		, B = 
3-2
53
 		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
42
 		, B = 
4-2
41
 		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 = 
62
31
 		, B = 
4-2
32
 		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
22
 		, B = 
4-2
41
 		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 = 
42
34
 		, B = 
3-2
43
 		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 = 
12
33
 		, B = 
3-2
21
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
12
33
 		, B = 
3-2
21
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
1 2
3 3
+
3-2
21
= 
40
54
 		....(1)
B+A
3 -2
2 1
+
12
33
= 
40
54
 		....(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

 

 

 



2)  

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


If A = 
62
43
 		, B = 
1-2
22
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
62
43
 		, B = 
1-2
22
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
6 2
4 3
+
1-2
22
= 
70
65
 		....(1)
B+A
1 -2
2 2
+
62
43
= 
70
65
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
62
43
 +
-6-2
-4-3
= 
00
00
= O ...(3)
(-A) + A
-6-2
-4-3
 +

 

62
43

 

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

(i) To prove:   A+B = B+A

A+B
 
1 2
3 3
+
1-2
33
= 
20
66
 		....(1)
B+A
1 -2
3 3
+
12
33
= 
20
66
 		....(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

 

 

 



4)  

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


If A = 
42
41
 		, 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 = 
42
41
 		, B = 
3-2
34
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
4 2
4 1
+
3-2
34
= 
70
75
 		....(1)
B+A
3 -2
3 4
+
42
41
= 
70
75
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
42
41
 +
-4-2
-4-1
= 
00
00
= O ...(3)
(-A) + A
-4-2
-4-1
 +

 

42
41

 

= 
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 = 
22
34
 		, B = 
4-2
35
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
22
34
 		, B = 
4-2
35
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
2 2
3 4
+
4-2
35
= 
60
69
 		....(1)
B+A
4 -2
3 5
+
22
34
= 
60
69
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
22
34
 +
-2-2
-3-4
= 
00
00
= O ...(3)
(-A) + A
-2-2
-3-4
 +

 

22
34

 

= 
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
33
 		, B = 
3-2
53
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
32
33
 		, B = 
3-2
53
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
3 2
3 3
+
3-2
53
= 
60
86
 		....(1)
B+A
3 -2
5 3
+
32
33
= 
60
86
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
32
33
 +
-3-2
-3-3
= 
00
00
= O ...(3)
(-A) + A
-3-2
-3-3
 +

 

32
33

 

= 
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
42
 		, B = 
4-2
41
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
62
42
 		, B = 
4-2
41
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
6 2
4 2
+
4-2
41
= 
100
83
 		....(1)
B+A
4 -2
4 1
+
62
42
= 
100
83
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
62
42
 +
-6-2
-4-2
= 
00
00
= O ...(3)
(-A) + A
-6-2
-4-2
 +

 

62
42

 

= 
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 = 
62
31
 		, B = 
4-2
32
 		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
32
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
6 2
3 1
+
4-2
32
= 
100
63
 		....(1)
B+A
4 -2
3 2
+
62
31
= 
100
63
 		....(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

 

 

 



9)  

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


If A = 
42
22
 		, B = 
4-2
41
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
42
22
 		, B = 
4-2
41
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
4 2
2 2
+
4-2
41
= 
80
63
 		....(1)
B+A
4 -2
4 1
+
42
22
= 
80
63
 		....(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

 

 

 



10)  

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


If A = 
42
34
 		, B = 
3-2
43
 		and O = 
00
00
 

(i)  A+B = Answer: B+A  

(ii)  A+(-A) = O Answer: (-A)+A

 


SOLUTION 1 :

 Given:

 

A = 
42
34
 		, B = 
3-2
43
 		and O = 
00
00
 

(i) To prove:   A+B = B+A

A+B
 
4 2
3 4
+
3-2
43
= 
70
77
 		....(1)
B+A
3 -2
4 3
+
42
34
= 
70
77
 		....(2)

 From (1) and (2)

A+B = B+A.

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

A+ (-A)
42
34
 +
-4-2
-3-4
= 
00
00
= O ...(3)
(-A) + A
-4-2
-3-4
 +

 

42
34

 

= 
00
00
 		= O...(4)

From (3) and (4) 

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