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 = 
34
43
 
B= 
6-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
24
53
 
B= 
6-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
54
45
 
B= 
5-2
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
23
44
 
B= 
6-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
44
63
 
B= 
4-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
53
44
 
B= 
4-3
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
55
72
 
B= 
6-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
24
65
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
35
32
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
24
55
 
B= 
4-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
34
43
 
B= 
6-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 18
Answer: 5 Answer: 2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
34
43
 
B= 
6-1
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
34
43
 
6-1
-22
 
= 
18+-8-3+8
24+-6-4+6
 
= 
105
182
 

 

(AB)T = 
1018
52
 
.............(1)

To Find BTAT

BT = 
6-2
-12
 
AT = 
34
43
 

 

BTAT=
6-2
-12
 
34
43
 
= 
18-824-6
-3+8-4+6
 
= 
1018
52
 
.......(2)

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

 



2)  
If  A = 
24
53
 
B= 
6-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 4 Answer: 24
Answer: 12 Answer: 2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
53
 
B= 
6-2
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
53
 
6-2
-24
 
= 
12+-8-4+16
30+-6-10+12
 
= 
412
242
 

 

(AB)T = 
424
122
 
.............(1)

To Find BTAT

BT = 
6-2
-24
 
AT = 
25
43
 

 

BTAT=
6-2
-24
 
25
43
 
= 
12-830-6
-4+16-10+12
 
= 
424
122
 
.......(2)

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

 



3)  
If  A = 
54
45
 
B= 
5-2
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 21 Answer: 15
Answer: -6 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
45
 
B= 
5-2
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
45
 
5-2
-11
 
= 
25+-4-10+4
20+-5-8+5
 
= 
21-6
15-3
 

 

(AB)T = 
2115
-6-3
 
.............(1)

To Find BTAT

BT = 
5-1
-21
 
AT = 
54
45
 

 

BTAT=
5-1
-21
 
54
45
 
= 
25-420-5
-10+4-8+5
 
= 
2115
-6-3
 
.......(2)

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

 



4)  
If  A = 
23
44
 
B= 
6-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 16
Answer: 10 Answer: 12
 
 






SOLUTION 1 :

 Given:

 

If  A = 
23
44
 
B= 
6-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
23
44
 
6-1
-24
 
= 
12+-6-2+12
24+-8-4+16
 
= 
610
1612
 

 

(AB)T = 
616
1012
 
.............(1)

To Find BTAT

BT = 
6-2
-14
 
AT = 
24
34
 

 

BTAT=
6-2
-14
 
24
34
 
= 
12-624-8
-2+12-4+16
 
= 
616
1012
 
.......(2)

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

 



5)  
If  A = 
44
63
 
B= 
4-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 18
Answer: -8 Answer: -15
 
 






SOLUTION 1 :

 Given:

 

If  A = 
44
63
 
B= 
4-3
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
44
63
 
4-3
-21
 
= 
16+-8-12+4
24+-6-18+3
 
= 
8-8
18-15
 

 

(AB)T = 
818
-8-15
 
.............(1)

To Find BTAT

BT = 
4-2
-31
 
AT = 
46
43
 

 

BTAT=
4-2
-31
 
46
43
 
= 
16-824-6
-12+4-18+3
 
= 
818
-8-15
 
.......(2)

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

 



6)  
If  A = 
53
44
 
B= 
4-3
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 8
Answer: -6 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
44
 
B= 
4-3
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
44
 
4-3
-23
 
= 
20+-6-15+9
16+-8-12+12
 
= 
14-6
80
 

 

(AB)T = 
148
-60
 
.............(1)

To Find BTAT

BT = 
4-2
-33
 
AT = 
54
34
 

 

BTAT=
4-2
-33
 
54
34
 
= 
20-616-8
-15+9-12+12
 
= 
148
-60
 
.......(2)

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

 



7)  
If  A = 
55
72
 
B= 
6-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 20 Answer: 38
Answer: 5 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
72
 
B= 
6-1
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
72
 
6-1
-22
 
= 
30+-10-5+10
42+-4-7+4
 
= 
205
38-3
 

 

(AB)T = 
2038
5-3
 
.............(1)

To Find BTAT

BT = 
6-2
-12
 
AT = 
57
52
 

 

BTAT=
6-2
-12
 
57
52
 
= 
30-1042-4
-5+10-7+4
 
= 
2038
5-3
 
.......(2)

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

 



8)  
If  A = 
24
65
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 2 Answer: 20
Answer: 10 Answer: 9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
65
 
B= 
5-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
65
 
5-1
-23
 
= 
10+-8-2+12
30+-10-6+15
 
= 
210
209
 

 

(AB)T = 
220
109
 
.............(1)

To Find BTAT

BT = 
5-2
-13
 
AT = 
26
45
 

 

BTAT=
5-2
-13
 
26
45
 
= 
10-830-10
-2+12-6+15
 
= 
220
109
 
.......(2)

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

 



9)  
If  A = 
35
32
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 14
Answer: 9 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
32
 
B= 
6-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
32
 
6-2
-23
 
= 
18+-10-6+15
18+-4-6+6
 
= 
89
140
 

 

(AB)T = 
814
90
 
.............(1)

To Find BTAT

BT = 
6-2
-23
 
AT = 
33
52
 

 

BTAT=
6-2
-23
 
33
52
 
= 
18-1018-4
-6+15-6+6
 
= 
814
90
 
.......(2)

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

 



10)  
If  A = 
24
55
 
B= 
4-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 4 Answer: 15
Answer: 10 Answer: 10
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
55
 
B= 
4-1
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
55
 
4-1
-13
 
= 
8+-4-2+12
20+-5-5+15
 
= 
410
1510
 

 

(AB)T = 
415
1010
 
.............(1)

To Find BTAT

BT = 
4-1
-13
 
AT = 
25
45
 

 

BTAT=
4-1
-13
 
25
45
 
= 
8-420-5
-2+12-5+15
 
= 
415
1010
 
.......(2)

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