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 = 
53
72
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
55
42
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
43
53
 
B= 
4-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
43
63
 
B= 
5-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
22
42
 
B= 
6-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
33
52
 
B= 
5-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
24
75
 
B= 
5-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
23
63
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
33
64
 
B= 
6-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
24
34
 
B= 
4-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
53
72
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 17 Answer: 26
Answer: 1 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
72
 
B= 
4-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
72
 
4-1
-12
 
= 
20+-3-5+6
28+-2-7+4
 
= 
171
26-3
 

 

(AB)T = 
1726
1-3
 
.............(1)

To Find BTAT

BT = 
4-1
-12
 
AT = 
57
32
 

 

BTAT=
4-1
-12
 
57
32
 
= 
20-328-2
-5+6-7+4
 
= 
1726
1-3
 
.......(2)

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

 



2)  
If  A = 
55
42
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 20 Answer: 20
Answer: 5 Answer: -2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
42
 
B= 
6-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
42
 
6-2
-23
 
= 
30+-10-10+15
24+-4-8+6
 
= 
205
20-2
 

 

(AB)T = 
2020
5-2
 
.............(1)

To Find BTAT

BT = 
6-2
-23
 
AT = 
54
52
 

 

BTAT=
6-2
-23
 
54
52
 
= 
30-1024-4
-10+15-8+6
 
= 
2020
5-2
 
.......(2)

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

 



3)  
If  A = 
43
53
 
B= 
4-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 13 Answer: 17
Answer: 1 Answer: -1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
53
 
B= 
4-2
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
53
 
4-2
-13
 
= 
16+-3-8+9
20+-3-10+9
 
= 
131
17-1
 

 

(AB)T = 
1317
1-1
 
.............(1)

To Find BTAT

BT = 
4-1
-23
 
AT = 
45
33
 

 

BTAT=
4-1
-23
 
45
33
 
= 
16-320-3
-8+9-10+9
 
= 
1317
1-1
 
.......(2)

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

 



4)  
If  A = 
43
63
 
B= 
5-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 17 Answer: 27
Answer: -9 Answer: -15
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
63
 
B= 
5-3
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
63
 
5-3
-11
 
= 
20+-3-12+3
30+-3-18+3
 
= 
17-9
27-15
 

 

(AB)T = 
1727
-9-15
 
.............(1)

To Find BTAT

BT = 
5-1
-31
 
AT = 
46
33
 

 

BTAT=
5-1
-31
 
46
33
 
= 
20-330-3
-12+3-18+3
 
= 
1727
-9-15
 
.......(2)

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

 



5)  
If  A = 
22
42
 
B= 
6-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 20
Answer: 2 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
42
 
B= 
6-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
42
 
6-3
-24
 
= 
12+-4-6+8
24+-4-12+8
 
= 
82
20-4
 

 

(AB)T = 
820
2-4
 
.............(1)

To Find BTAT

BT = 
6-2
-34
 
AT = 
24
22
 

 

BTAT=
6-2
-34
 
24
22
 
= 
12-424-4
-6+8-12+8
 
= 
820
2-4
 
.......(2)

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

 



6)  
If  A = 
33
52
 
B= 
5-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 23
Answer: 9 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
33
52
 
B= 
5-1
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
33
52
 
5-1
-14
 
= 
15+-3-3+12
25+-2-5+8
 
= 
129
233
 

 

(AB)T = 
1223
93
 
.............(1)

To Find BTAT

BT = 
5-1
-14
 
AT = 
35
32
 

 

BTAT=
5-1
-14
 
35
32
 
= 
15-325-2
-3+12-5+8
 
= 
1223
93
 
.......(2)

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

 



7)  
If  A = 
24
75
 
B= 
5-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 30
Answer: 14 Answer: 13
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
75
 
B= 
5-1
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
75
 
5-1
-14
 
= 
10+-4-2+16
35+-5-7+20
 
= 
614
3013
 

 

(AB)T = 
630
1413
 
.............(1)

To Find BTAT

BT = 
5-1
-14
 
AT = 
27
45
 

 

BTAT=
5-1
-14
 
27
45
 
= 
10-435-5
-2+16-7+20
 
= 
630
1413
 
.......(2)

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

 



8)  
If  A = 
23
63
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 9 Answer: 33
Answer: 0 Answer: -12
 
 






SOLUTION 1 :

 Given:

 

If  A = 
23
63
 
B= 
6-3
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
23
63
 
6-3
-12
 
= 
12+-3-6+6
36+-3-18+6
 
= 
90
33-12
 

 

(AB)T = 
933
0-12
 
.............(1)

To Find BTAT

BT = 
6-1
-32
 
AT = 
26
33
 

 

BTAT=
6-1
-32
 
26
33
 
= 
12-336-3
-6+6-18+6
 
= 
933
0-12
 
.......(2)

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

 



9)  
If  A = 
33
64
 
B= 
6-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 15 Answer: 32
Answer: -6 Answer: -14
 
 






SOLUTION 1 :

 Given:

 

If  A = 
33
64
 
B= 
6-3
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
33
64
 
6-3
-11
 
= 
18+-3-9+3
36+-4-18+4
 
= 
15-6
32-14
 

 

(AB)T = 
1532
-6-14
 
.............(1)

To Find BTAT

BT = 
6-1
-31
 
AT = 
36
34
 

 

BTAT=
6-1
-31
 
36
34
 
= 
18-336-4
-9+3-18+4
 
= 
1532
-6-14
 
.......(2)

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

 



10)  
If  A = 
24
34
 
B= 
4-1
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 0 Answer: 4
Answer: 2 Answer: 1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
34
 
B= 
4-1
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
34
 
4-1
-21
 
= 
8+-8-2+4
12+-8-3+4
 
= 
02
41
 

 

(AB)T = 
04
21
 
.............(1)

To Find BTAT

BT = 
4-2
-11
 
AT = 
23
44
 

 

BTAT=
4-2
-11
 
23
44
 
= 
8-812-8
-2+4-3+4
 
= 
04
21
 
.......(2)

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