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 = 
55
63
 
B= 
6-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
35
75
 
B= 
6-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
54
62
 
B= 
4-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
32
45
 
B= 
4-3
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
32
75
 
B= 
4-2
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
42
73
 
B= 
4-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
24
54
 
B= 
6-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
55
44
 
B= 
5-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
23
33
 
B= 
4-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
33
42
 
B= 
4-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
55
63
 
B= 
6-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 20 Answer: 30
Answer: 0 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
63
 
B= 
6-1
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
63
 
6-1
-21
 
= 
30+-10-5+5
36+-6-6+3
 
= 
200
30-3
 

 

(AB)T = 
2030
0-3
 
.............(1)

To Find BTAT

BT = 
6-2
-11
 
AT = 
56
53
 

 

BTAT=
6-2
-11
 
56
53
 
= 
30-1036-6
-5+5-6+3
 
= 
2030
0-3
 
.......(2)

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

 



2)  
If  A = 
35
75
 
B= 
6-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 32
Answer: 4 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
75
 
B= 
6-2
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
75
 
6-2
-22
 
= 
18+-10-6+10
42+-10-14+10
 
= 
84
32-4
 

 

(AB)T = 
832
4-4
 
.............(1)

To Find BTAT

BT = 
6-2
-22
 
AT = 
37
55
 

 

BTAT=
6-2
-22
 
37
55
 
= 
18-1042-10
-6+10-14+10
 
= 
832
4-4
 
.......(2)

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

 



3)  
If  A = 
54
62
 
B= 
4-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 20
Answer: -1 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
62
 
B= 
4-1
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
62
 
4-1
-21
 
= 
20+-8-5+4
24+-4-6+2
 
= 
12-1
20-4
 

 

(AB)T = 
1220
-1-4
 
.............(1)

To Find BTAT

BT = 
4-2
-11
 
AT = 
56
42
 

 

BTAT=
4-2
-11
 
56
42
 
= 
20-824-4
-5+4-6+2
 
= 
1220
-1-4
 
.......(2)

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

 



4)  
If  A = 
32
45
 
B= 
4-3
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 6
Answer: -3 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
45
 
B= 
4-3
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
45
 
4-3
-23
 
= 
12+-4-9+6
16+-10-12+15
 
= 
8-3
63
 

 

(AB)T = 
86
-33
 
.............(1)

To Find BTAT

BT = 
4-2
-33
 
AT = 
34
25
 

 

BTAT=
4-2
-33
 
34
25
 
= 
12-416-10
-9+6-12+15
 
= 
86
-33
 
.......(2)

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

 



5)  
If  A = 
32
75
 
B= 
4-2
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 23
Answer: 2 Answer: 6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
75
 
B= 
4-2
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
75
 
4-2
-14
 
= 
12+-2-6+8
28+-5-14+20
 
= 
102
236
 

 

(AB)T = 
1023
26
 
.............(1)

To Find BTAT

BT = 
4-1
-24
 
AT = 
37
25
 

 

BTAT=
4-1
-24
 
37
25
 
= 
12-228-5
-6+8-14+20
 
= 
1023
26
 
.......(2)

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

 



6)  
If  A = 
42
73
 
B= 
4-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 22
Answer: 0 Answer: -1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
42
73
 
B= 
4-1
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
42
73
 
4-1
-22
 
= 
16+-4-4+4
28+-6-7+6
 
= 
120
22-1
 

 

(AB)T = 
1222
0-1
 
.............(1)

To Find BTAT

BT = 
4-2
-12
 
AT = 
47
23
 

 

BTAT=
4-2
-12
 
47
23
 
= 
16-428-6
-4+4-7+6
 
= 
1222
0-1
 
.......(2)

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

 



7)  
If  A = 
24
54
 
B= 
6-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 26
Answer: -2 Answer: -11
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
54
 
B= 
6-3
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
54
 
6-3
-11
 
= 
12+-4-6+4
30+-4-15+4
 
= 
8-2
26-11
 

 

(AB)T = 
826
-2-11
 
.............(1)

To Find BTAT

BT = 
6-1
-31
 
AT = 
25
44
 

 

BTAT=
6-1
-31
 
25
44
 
= 
12-430-4
-6+4-15+4
 
= 
826
-2-11
 
.......(2)

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

 



8)  
If  A = 
55
44
 
B= 
5-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 15 Answer: 12
Answer: 0 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
44
 
B= 
5-1
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
44
 
5-1
-21
 
= 
25+-10-5+5
20+-8-4+4
 
= 
150
120
 

 

(AB)T = 
1512
00
 
.............(1)

To Find BTAT

BT = 
5-2
-11
 
AT = 
54
54
 

 

BTAT=
5-2
-11
 
54
54
 
= 
25-1020-8
-5+5-4+4
 
= 
1512
00
 
.......(2)

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

 



9)  
If  A = 
23
33
 
B= 
4-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 2 Answer: 6
Answer: 6 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
23
33
 
B= 
4-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
23
33
 
4-3
-24
 
= 
8+-6-6+12
12+-6-9+12
 
= 
26
63
 

 

(AB)T = 
26
63
 
.............(1)

To Find BTAT

BT = 
4-2
-34
 
AT = 
23
33
 

 

BTAT=
4-2
-34
 
23
33
 
= 
8-612-6
-6+12-9+12
 
= 
26
63
 
.......(2)

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

 



10)  
If  A = 
33
42
 
B= 
4-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 9 Answer: 14
Answer: -3 Answer: -8
 
 






SOLUTION 1 :

 Given:

 

If  A = 
33
42
 
B= 
4-3
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
33
42
 
4-3
-12
 
= 
12+-3-9+6
16+-2-12+4
 
= 
9-3
14-8
 

 

(AB)T = 
914
-3-8
 
.............(1)

To Find BTAT

BT = 
4-1
-32
 
AT = 
34
32
 

 

BTAT=
4-1
-32
 
34
32
 
= 
12-316-2
-9+6-12+4
 
= 
914
-3-8
 
.......(2)

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