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 = 
42
63
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
23
73
 
B= 
6-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
34
52
 
B= 
6-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
53
53
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
25
35
 
B= 
5-2
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
44
73
 
B= 
5-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
53
44
 
B= 
6-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
35
72
 
B= 
5-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
53
52
 
B= 
4-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
25
35
 
B= 
5-2
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
42
63
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 22 Answer: 33
Answer: -2 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
42
63
 
B= 
6-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
42
63
 
6-1
-11
 
= 
24+-2-4+2
36+-3-6+3
 
= 
22-2
33-3
 

 

(AB)T = 
2233
-2-3
 
.............(1)

To Find BTAT

BT = 
6-1
-11
 
AT = 
46
23
 

 

BTAT=
6-1
-11
 
46
23
 
= 
24-236-3
-4+2-6+3
 
= 
2233
-2-3
 
.......(2)

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

 



2)  
If  A = 
23
73
 
B= 
6-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 36
Answer: -1 Answer: -11
 
 






SOLUTION 1 :

 Given:

 

If  A = 
23
73
 
B= 
6-2
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
23
73
 
6-2
-21
 
= 
12+-6-4+3
42+-6-14+3
 
= 
6-1
36-11
 

 

(AB)T = 
636
-1-11
 
.............(1)

To Find BTAT

BT = 
6-2
-21
 
AT = 
27
33
 

 

BTAT=
6-2
-21
 
27
33
 
= 
12-642-6
-4+3-14+3
 
= 
636
-1-11
 
.......(2)

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

 



3)  
If  A = 
34
52
 
B= 
6-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 26
Answer: 1 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
34
52
 
B= 
6-1
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
34
52
 
6-1
-21
 
= 
18+-8-3+4
30+-4-5+2
 
= 
101
26-3
 

 

(AB)T = 
1026
1-3
 
.............(1)

To Find BTAT

BT = 
6-2
-11
 
AT = 
35
42
 

 

BTAT=
6-2
-11
 
35
42
 
= 
18-830-4
-3+4-5+2
 
= 
1026
1-3
 
.......(2)

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

 



4)  
If  A = 
53
53
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 19 Answer: 19
Answer: 4 Answer: 4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
53
 
B= 
5-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
53
 
5-1
-23
 
= 
25+-6-5+9
25+-6-5+9
 
= 
194
194
 

 

(AB)T = 
1919
44
 
.............(1)

To Find BTAT

BT = 
5-2
-13
 
AT = 
55
33
 

 

BTAT=
5-2
-13
 
55
33
 
= 
25-625-6
-5+9-5+9
 
= 
1919
44
 
.......(2)

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

 



5)  
If  A = 
25
35
 
B= 
5-2
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 10
Answer: 16 Answer: 14
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
35
 
B= 
5-2
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
35
 
5-2
-14
 
= 
10+-5-4+20
15+-5-6+20
 
= 
516
1014
 

 

(AB)T = 
510
1614
 
.............(1)

To Find BTAT

BT = 
5-1
-24
 
AT = 
23
55
 

 

BTAT=
5-1
-24
 
23
55
 
= 
10-515-5
-4+20-6+20
 
= 
510
1614
 
.......(2)

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

 



6)  
If  A = 
44
73
 
B= 
5-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 29
Answer: -4 Answer: -15
 
 






SOLUTION 1 :

 Given:

 

If  A = 
44
73
 
B= 
5-3
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
44
73
 
5-3
-22
 
= 
20+-8-12+8
35+-6-21+6
 
= 
12-4
29-15
 

 

(AB)T = 
1229
-4-15
 
.............(1)

To Find BTAT

BT = 
5-2
-32
 
AT = 
47
43
 

 

BTAT=
5-2
-32
 
47
43
 
= 
20-835-6
-12+8-21+6
 
= 
1229
-4-15
 
.......(2)

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

 



7)  
If  A = 
53
44
 
B= 
6-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 27 Answer: 20
Answer: 1 Answer: 4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
44
 
B= 
6-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
44
 
6-1
-12
 
= 
30+-3-5+6
24+-4-4+8
 
= 
271
204
 

 

(AB)T = 
2720
14
 
.............(1)

To Find BTAT

BT = 
6-1
-12
 
AT = 
54
34
 

 

BTAT=
6-1
-12
 
54
34
 
= 
30-324-4
-5+6-4+8
 
= 
2720
14
 
.......(2)

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

 



8)  
If  A = 
35
72
 
B= 
5-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 31
Answer: 2 Answer: -5
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
72
 
B= 
5-1
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
72
 
5-1
-21
 
= 
15+-10-3+5
35+-4-7+2
 
= 
52
31-5
 

 

(AB)T = 
531
2-5
 
.............(1)

To Find BTAT

BT = 
5-2
-11
 
AT = 
37
52
 

 

BTAT=
5-2
-11
 
37
52
 
= 
15-1035-4
-3+5-7+2
 
= 
531
2-5
 
.......(2)

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

 



9)  
If  A = 
53
52
 
B= 
4-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 16
Answer: -2 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
52
 
B= 
4-1
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
52
 
4-1
-21
 
= 
20+-6-5+3
20+-4-5+2
 
= 
14-2
16-3
 

 

(AB)T = 
1416
-2-3
 
.............(1)

To Find BTAT

BT = 
4-2
-11
 
AT = 
55
32
 

 

BTAT=
4-2
-11
 
55
32
 
= 
20-620-4
-5+3-5+2
 
= 
1416
-2-3
 
.......(2)

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

 



10)  
If  A = 
25
35
 
B= 
5-2
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 10
Answer: 1 Answer: -1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
35
 
B= 
5-2
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
35
 
5-2
-11
 
= 
10+-5-4+5
15+-5-6+5
 
= 
51
10-1
 

 

(AB)T = 
510
1-1
 
.............(1)

To Find BTAT

BT = 
5-1
-21
 
AT = 
23
55
 

 

BTAT=
5-1
-21
 
23
55
 
= 
10-515-5
-4+5-6+5
 
= 
510
1-1
 
.......(2)

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