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 = 
32
74
 
B= 
5-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
35
33
 
B= 
6-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
43
53
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
35
44
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
32
55
 
B= 
4-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
34
43
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
33
65
 
B= 
5-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
32
62
 
B= 
4-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
54
65
 
B= 
4-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
25
55
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
32
74
 
B= 
5-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 11 Answer: 27
Answer: 5 Answer: 9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
74
 
B= 
5-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
74
 
5-1
-24
 
= 
15+-4-3+8
35+-8-7+16
 
= 
115
279
 

 

(AB)T = 
1127
59
 
.............(1)

To Find BTAT

BT = 
5-2
-14
 
AT = 
37
24
 

 

BTAT=
5-2
-14
 
37
24
 
= 
15-435-8
-3+8-7+16
 
= 
1127
59
 
.......(2)

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

 



2)  
If  A = 
35
33
 
B= 
6-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 12
Answer: 11 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
33
 
B= 
6-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
33
 
6-3
-24
 
= 
18+-10-9+20
18+-6-9+12
 
= 
811
123
 

 

(AB)T = 
812
113
 
.............(1)

To Find BTAT

BT = 
6-2
-34
 
AT = 
33
53
 

 

BTAT=
6-2
-34
 
33
53
 
= 
18-1018-6
-9+20-9+12
 
= 
812
113
 
.......(2)

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

 



3)  
If  A = 
43
53
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 14
Answer: 8 Answer: 7
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
53
 
B= 
4-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
53
 
4-1
-24
 
= 
16+-6-4+12
20+-6-5+12
 
= 
108
147
 

 

(AB)T = 
1014
87
 
.............(1)

To Find BTAT

BT = 
4-2
-14
 
AT = 
45
33
 

 

BTAT=
4-2
-14
 
45
33
 
= 
16-620-6
-4+12-5+12
 
= 
1014
87
 
.......(2)

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

 



4)  
If  A = 
35
44
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 13 Answer: 20
Answer: 1 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
44
 
B= 
6-3
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
44
 
6-3
-12
 
= 
18+-5-9+10
24+-4-12+8
 
= 
131
20-4
 

 

(AB)T = 
1320
1-4
 
.............(1)

To Find BTAT

BT = 
6-1
-32
 
AT = 
34
54
 

 

BTAT=
6-1
-32
 
34
54
 
= 
18-524-4
-9+10-12+8
 
= 
1320
1-4
 
.......(2)

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

 



5)  
If  A = 
32
55
 
B= 
4-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 10
Answer: 2 Answer: 10
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
55
 
B= 
4-2
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
55
 
4-2
-24
 
= 
12+-4-6+8
20+-10-10+20
 
= 
82
1010
 

 

(AB)T = 
810
210
 
.............(1)

To Find BTAT

BT = 
4-2
-24
 
AT = 
35
25
 

 

BTAT=
4-2
-24
 
35
25
 
= 
12-420-10
-6+8-10+20
 
= 
810
210
 
.......(2)

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

 



6)  
If  A = 
34
43
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 21
Answer: -1 Answer: -6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
34
43
 
B= 
6-3
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
34
43
 
6-3
-12
 
= 
18+-4-9+8
24+-3-12+6
 
= 
14-1
21-6
 

 

(AB)T = 
1421
-1-6
 
.............(1)

To Find BTAT

BT = 
6-1
-32
 
AT = 
34
43
 

 

BTAT=
6-1
-32
 
34
43
 
= 
18-424-3
-9+8-12+6
 
= 
1421
-1-6
 
.......(2)

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

 



7)  
If  A = 
33
65
 
B= 
5-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 25
Answer: 0 Answer: -1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
33
65
 
B= 
5-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
33
65
 
5-1
-11
 
= 
15+-3-3+3
30+-5-6+5
 
= 
120
25-1
 

 

(AB)T = 
1225
0-1
 
.............(1)

To Find BTAT

BT = 
5-1
-11
 
AT = 
36
35
 

 

BTAT=
5-1
-11
 
36
35
 
= 
15-330-5
-3+3-6+5
 
= 
1225
0-1
 
.......(2)

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

 



8)  
If  A = 
32
62
 
B= 
4-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 22
Answer: -7 Answer: -16
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
62
 
B= 
4-3
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
62
 
4-3
-11
 
= 
12+-2-9+2
24+-2-18+2
 
= 
10-7
22-16
 

 

(AB)T = 
1022
-7-16
 
.............(1)

To Find BTAT

BT = 
4-1
-31
 
AT = 
36
22
 

 

BTAT=
4-1
-31
 
36
22
 
= 
12-224-2
-9+2-18+2
 
= 
1022
-7-16
 
.......(2)

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

 



9)  
If  A = 
54
65
 
B= 
4-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 14
Answer: -7 Answer: -8
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
65
 
B= 
4-3
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
65
 
4-3
-22
 
= 
20+-8-15+8
24+-10-18+10
 
= 
12-7
14-8
 

 

(AB)T = 
1214
-7-8
 
.............(1)

To Find BTAT

BT = 
4-2
-32
 
AT = 
56
45
 

 

BTAT=
4-2
-32
 
56
45
 
= 
20-824-10
-15+8-18+10
 
= 
1214
-7-8
 
.......(2)

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

 



10)  
If  A = 
25
55
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 0 Answer: 15
Answer: 13 Answer: 10
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
55
 
B= 
5-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
55
 
5-1
-23
 
= 
10+-10-2+15
25+-10-5+15
 
= 
013
1510
 

 

(AB)T = 
015
1310
 
.............(1)

To Find BTAT

BT = 
5-2
-13
 
AT = 
25
55
 

 

BTAT=
5-2
-13
 
25
55
 
= 
10-1025-10
-2+15-5+15
 
= 
015
1310
 
.......(2)

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