Scroll:matrices >> Transpose of matrix >> ps (4147)


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)  
If  A = 
35
75
 
B= 
5-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
54
52
 
B= 
5-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
42
74
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
25
73
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
22
63
 
B= 
4-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
54
65
 
B= 
4-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
44
62
 
B= 
5-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
54
44
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
32
72
 
B= 
6-3
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
44
43
 
B= 
6-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
35
75
 
B= 
5-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 25
Answer: -4 Answer: -16
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
75
 
B= 
5-3
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
75
 
5-3
-21
 
= 
15+-10-9+5
35+-10-21+5
 
= 
5-4
25-16
 

 

(AB)T = 
525
-4-16
 
.............(1)

To Find BTAT

BT = 
5-2
-31
 
AT = 
37
55
 

 

BTAT=
5-2
-31
 
37
55
 
= 
15-1035-10
-9+5-21+5
 
= 
525
-4-16
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



2)  
If  A = 
54
52
 
B= 
5-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 21 Answer: 23
Answer: 3 Answer: -1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
52
 
B= 
5-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
52
 
5-1
-12
 
= 
25+-4-5+8
25+-2-5+4
 
= 
213
23-1
 

 

(AB)T = 
2123
3-1
 
.............(1)

To Find BTAT

BT = 
5-1
-12
 
AT = 
55
42
 

 

BTAT=
5-1
-12
 
55
42
 
= 
25-425-2
-5+8-5+4
 
= 
2123
3-1
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



3)  
If  A = 
42
74
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 20
Answer: 4 Answer: 9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
42
74
 
B= 
4-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
42
74
 
4-1
-24
 
= 
16+-4-4+8
28+-8-7+16
 
= 
124
209
 

 

(AB)T = 
1220
49
 
.............(1)

To Find BTAT

BT = 
4-2
-14
 
AT = 
47
24
 

 

BTAT=
4-2
-14
 
47
24
 
= 
16-428-8
-4+8-7+16
 
= 
1220
49
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



4)  
If  A = 
25
73
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 7 Answer: 39
Answer: 3 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
73
 
B= 
6-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
73
 
6-1
-11
 
= 
12+-5-2+5
42+-3-7+3
 
= 
73
39-4
 

 

(AB)T = 
739
3-4
 
.............(1)

To Find BTAT

BT = 
6-1
-11
 
AT = 
27
53
 

 

BTAT=
6-1
-11
 
27
53
 
= 
12-542-3
-2+5-7+3
 
= 
739
3-4
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



5)  
If  A = 
22
63
 
B= 
4-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 4 Answer: 18
Answer: 2 Answer: -6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
63
 
B= 
4-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
63
 
4-3
-24
 
= 
8+-4-6+8
24+-6-18+12
 
= 
42
18-6
 

 

(AB)T = 
418
2-6
 
.............(1)

To Find BTAT

BT = 
4-2
-34
 
AT = 
26
23
 

 

BTAT=
4-2
-34
 
26
23
 
= 
8-424-6
-6+8-18+12
 
= 
418
2-6
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



6)  
If  A = 
54
65
 
B= 
4-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 16 Answer: 19
Answer: 2 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
65
 
B= 
4-2
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
65
 
4-2
-13
 
= 
20+-4-10+12
24+-5-12+15
 
= 
162
193
 

 

(AB)T = 
1619
23
 
.............(1)

To Find BTAT

BT = 
4-1
-23
 
AT = 
56
45
 

 

BTAT=
4-1
-23
 
56
45
 
= 
20-424-5
-10+12-12+15
 
= 
1619
23
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



7)  
If  A = 
44
62
 
B= 
5-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 16 Answer: 28
Answer: 4 Answer: -2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
44
62
 
B= 
5-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
44
62
 
5-1
-12
 
= 
20+-4-4+8
30+-2-6+4
 
= 
164
28-2
 

 

(AB)T = 
1628
4-2
 
.............(1)

To Find BTAT

BT = 
5-1
-12
 
AT = 
46
42
 

 

BTAT=
5-1
-12
 
46
42
 
= 
20-430-2
-4+8-6+4
 
= 
1628
4-2
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



8)  
If  A = 
54
44
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 16 Answer: 12
Answer: 3 Answer: 4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
44
 
B= 
4-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
44
 
4-1
-12
 
= 
20+-4-5+8
16+-4-4+8
 
= 
163
124
 

 

(AB)T = 
1612
34
 
.............(1)

To Find BTAT

BT = 
4-1
-12
 
AT = 
54
44
 

 

BTAT=
4-1
-12
 
54
44
 
= 
20-416-4
-5+8-4+8
 
= 
1612
34
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



9)  
If  A = 
32
72
 
B= 
6-3
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 38
Answer: -3 Answer: -15
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
72
 
B= 
6-3
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
72
 
6-3
-23
 
= 
18+-4-9+6
42+-4-21+6
 
= 
14-3
38-15
 

 

(AB)T = 
1438
-3-15
 
.............(1)

To Find BTAT

BT = 
6-2
-33
 
AT = 
37
22
 

 

BTAT=
6-2
-33
 
37
22
 
= 
18-442-4
-9+6-21+6
 
= 
1438
-3-15
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.

 



10)  
If  A = 
44
43
 
B= 
6-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 20 Answer: 21
Answer: -8 Answer: -9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
44
43
 
B= 
6-3
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
44
43
 
6-3
-11
 
= 
24+-4-12+4
24+-3-12+3
 
= 
20-8
21-9
 

 

(AB)T = 
2021
-8-9
 
.............(1)

To Find BTAT

BT = 
6-1
-31
 
AT = 
44
43
 

 

BTAT=
6-1
-31
 
44
43
 
= 
24-424-3
-12+4-12+3
 
= 
2021
-8-9
 
.......(2)

From (1) and (2) We get (AB)T =  BTAT.