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 = 
54
33
 
B= 
4-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
33
54
 
B= 
6-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
55
53
 
B= 
4-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
52
55
 
B= 
4-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
53
64
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
45
32
 
B= 
4-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
35
42
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
43
74
 
B= 
4-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
54
43
 
B= 
5-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
22
54
 
B= 
5-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
54
33
 
B= 
4-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 6
Answer: -11 Answer: -6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
33
 
B= 
4-3
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
33
 
4-3
-21
 
= 
20+-8-15+4
12+-6-9+3
 
= 
12-11
6-6
 

 

(AB)T = 
126
-11-6
 
.............(1)

To Find BTAT

BT = 
4-2
-31
 
AT = 
53
43
 

 

BTAT=
4-2
-31
 
53
43
 
= 
20-812-6
-15+4-9+3
 
= 
126
-11-6
 
.......(2)

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

 



2)  
If  A = 
33
54
 
B= 
6-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 15 Answer: 26
Answer: 3 Answer: 1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
33
54
 
B= 
6-3
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
33
54
 
6-3
-14
 
= 
18+-3-9+12
30+-4-15+16
 
= 
153
261
 

 

(AB)T = 
1526
31
 
.............(1)

To Find BTAT

BT = 
6-1
-34
 
AT = 
35
34
 

 

BTAT=
6-1
-34
 
35
34
 
= 
18-330-4
-9+12-15+16
 
= 
1526
31
 
.......(2)

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

 



3)  
If  A = 
55
53
 
B= 
4-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 15 Answer: 17
Answer: 15 Answer: 7
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
53
 
B= 
4-1
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
53
 
4-1
-14
 
= 
20+-5-5+20
20+-3-5+12
 
= 
1515
177
 

 

(AB)T = 
1517
157
 
.............(1)

To Find BTAT

BT = 
4-1
-14
 
AT = 
55
53
 

 

BTAT=
4-1
-14
 
55
53
 
= 
20-520-3
-5+20-5+12
 
= 
1517
157
 
.......(2)

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

 



4)  
If  A = 
52
55
 
B= 
4-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 18 Answer: 15
Answer: -7 Answer: 5
 
 






SOLUTION 1 :

 Given:

 

If  A = 
52
55
 
B= 
4-3
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
52
55
 
4-3
-14
 
= 
20+-2-15+8
20+-5-15+20
 
= 
18-7
155
 

 

(AB)T = 
1815
-75
 
.............(1)

To Find BTAT

BT = 
4-1
-34
 
AT = 
55
25
 

 

BTAT=
4-1
-34
 
55
25
 
= 
20-220-5
-15+8-15+20
 
= 
1815
-75
 
.......(2)

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

 



5)  
If  A = 
53
64
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 27 Answer: 32
Answer: -2 Answer: -2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
64
 
B= 
6-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
64
 
6-1
-11
 
= 
30+-3-5+3
36+-4-6+4
 
= 
27-2
32-2
 

 

(AB)T = 
2732
-2-2
 
.............(1)

To Find BTAT

BT = 
6-1
-11
 
AT = 
56
34
 

 

BTAT=
6-1
-11
 
56
34
 
= 
30-336-4
-5+3-6+4
 
= 
2732
-2-2
 
.......(2)

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

 



6)  
If  A = 
45
32
 
B= 
4-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 11 Answer: 10
Answer: 7 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
45
32
 
B= 
4-2
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
45
32
 
4-2
-13
 
= 
16+-5-8+15
12+-2-6+6
 
= 
117
100
 

 

(AB)T = 
1110
70
 
.............(1)

To Find BTAT

BT = 
4-1
-23
 
AT = 
43
52
 

 

BTAT=
4-1
-23
 
43
52
 
= 
16-512-2
-8+15-6+6
 
= 
1110
70
 
.......(2)

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

 



7)  
If  A = 
35
42
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 20
Answer: 9 Answer: -2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
42
 
B= 
6-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
42
 
6-2
-23
 
= 
18+-10-6+15
24+-4-8+6
 
= 
89
20-2
 

 

(AB)T = 
820
9-2
 
.............(1)

To Find BTAT

BT = 
6-2
-23
 
AT = 
34
52
 

 

BTAT=
6-2
-23
 
34
52
 
= 
18-1024-4
-6+15-8+6
 
= 
820
9-2
 
.......(2)

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

 



8)  
If  A = 
43
74
 
B= 
4-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 20
Answer: 1 Answer: -2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
74
 
B= 
4-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
74
 
4-2
-23
 
= 
16+-6-8+9
28+-8-14+12
 
= 
101
20-2
 

 

(AB)T = 
1020
1-2
 
.............(1)

To Find BTAT

BT = 
4-2
-23
 
AT = 
47
34
 

 

BTAT=
4-2
-23
 
47
34
 
= 
16-628-8
-8+9-14+12
 
= 
1020
1-2
 
.......(2)

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

 



9)  
If  A = 
54
43
 
B= 
5-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 21 Answer: 17
Answer: 11 Answer: 8
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
43
 
B= 
5-1
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
43
 
5-1
-14
 
= 
25+-4-5+16
20+-3-4+12
 
= 
2111
178
 

 

(AB)T = 
2117
118
 
.............(1)

To Find BTAT

BT = 
5-1
-14
 
AT = 
54
43
 

 

BTAT=
5-1
-14
 
54
43
 
= 
25-420-3
-5+16-4+12
 
= 
2117
118
 
.......(2)

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

 



10)  
If  A = 
22
54
 
B= 
5-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 17
Answer: -2 Answer: -6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
54
 
B= 
5-2
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
54
 
5-2
-21
 
= 
10+-4-4+2
25+-8-10+4
 
= 
6-2
17-6
 

 

(AB)T = 
617
-2-6
 
.............(1)

To Find BTAT

BT = 
5-2
-21
 
AT = 
25
24
 

 

BTAT=
5-2
-21
 
25
24
 
= 
10-425-8
-4+2-10+4
 
= 
617
-2-6
 
.......(2)

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