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 = 
22
53
 
B= 
4-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
22
32
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
45
45
 
B= 
6-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
35
45
 
B= 
5-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
52
73
 
B= 
6-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
34
75
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
53
33
 
B= 
4-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
23
64
 
B= 
6-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
45
34
 
B= 
4-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
35
65
 
B= 
5-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
22
53
 
B= 
4-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 17
Answer: 0 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
53
 
B= 
4-2
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
53
 
4-2
-12
 
= 
8+-2-4+4
20+-3-10+6
 
= 
60
17-4
 

 

(AB)T = 
617
0-4
 
.............(1)

To Find BTAT

BT = 
4-1
-22
 
AT = 
25
23
 

 

BTAT=
4-1
-22
 
25
23
 
= 
8-220-3
-4+4-10+6
 
= 
617
0-4
 
.......(2)

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

 



2)  
If  A = 
22
32
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 14
Answer: 2 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
32
 
B= 
6-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
32
 
6-2
-23
 
= 
12+-4-4+6
18+-4-6+6
 
= 
82
140
 

 

(AB)T = 
814
20
 
.............(1)

To Find BTAT

BT = 
6-2
-23
 
AT = 
23
22
 

 

BTAT=
6-2
-23
 
23
22
 
= 
12-418-4
-4+6-6+6
 
= 
814
20
 
.......(2)

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

 



3)  
If  A = 
45
45
 
B= 
6-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 14
Answer: 6 Answer: 6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
45
45
 
B= 
6-1
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
45
45
 
6-1
-22
 
= 
24+-10-4+10
24+-10-4+10
 
= 
146
146
 

 

(AB)T = 
1414
66
 
.............(1)

To Find BTAT

BT = 
6-2
-12
 
AT = 
44
55
 

 

BTAT=
6-2
-12
 
44
55
 
= 
24-1024-10
-4+10-4+10
 
= 
1414
66
 
.......(2)

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

 



4)  
If  A = 
35
45
 
B= 
5-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 10
Answer: 14 Answer: 12
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
45
 
B= 
5-2
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
45
 
5-2
-24
 
= 
15+-10-6+20
20+-10-8+20
 
= 
514
1012
 

 

(AB)T = 
510
1412
 
.............(1)

To Find BTAT

BT = 
5-2
-24
 
AT = 
34
55
 

 

BTAT=
5-2
-24
 
34
55
 
= 
15-1020-10
-6+20-8+20
 
= 
510
1412
 
.......(2)

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

 



5)  
If  A = 
52
73
 
B= 
6-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 26 Answer: 36
Answer: -8 Answer: -11
 
 






SOLUTION 1 :

 Given:

 

If  A = 
52
73
 
B= 
6-2
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
52
73
 
6-2
-21
 
= 
30+-4-10+2
42+-6-14+3
 
= 
26-8
36-11
 

 

(AB)T = 
2636
-8-11
 
.............(1)

To Find BTAT

BT = 
6-2
-21
 
AT = 
57
23
 

 

BTAT=
6-2
-21
 
57
23
 
= 
30-442-6
-10+2-14+3
 
= 
2636
-8-11
 
.......(2)

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

 



6)  
If  A = 
34
75
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 23
Answer: 5 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
34
75
 
B= 
4-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
34
75
 
4-1
-12
 
= 
12+-4-3+8
28+-5-7+10
 
= 
85
233
 

 

(AB)T = 
823
53
 
.............(1)

To Find BTAT

BT = 
4-1
-12
 
AT = 
37
45
 

 

BTAT=
4-1
-12
 
37
45
 
= 
12-428-5
-3+8-7+10
 
= 
823
53
 
.......(2)

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

 



7)  
If  A = 
53
33
 
B= 
4-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 6
Answer: -3 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
33
 
B= 
4-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
33
 
4-3
-24
 
= 
20+-6-15+12
12+-6-9+12
 
= 
14-3
63
 

 

(AB)T = 
146
-33
 
.............(1)

To Find BTAT

BT = 
4-2
-34
 
AT = 
53
33
 

 

BTAT=
4-2
-34
 
53
33
 
= 
20-612-6
-15+12-9+12
 
= 
146
-33
 
.......(2)

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

 



8)  
If  A = 
23
64
 
B= 
6-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 28
Answer: -1 Answer: -8
 
 






SOLUTION 1 :

 Given:

 

If  A = 
23
64
 
B= 
6-2
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
23
64
 
6-2
-21
 
= 
12+-6-4+3
36+-8-12+4
 
= 
6-1
28-8
 

 

(AB)T = 
628
-1-8
 
.............(1)

To Find BTAT

BT = 
6-2
-21
 
AT = 
26
34
 

 

BTAT=
6-2
-21
 
26
34
 
= 
12-636-8
-4+3-12+4
 
= 
628
-1-8
 
.......(2)

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

 



9)  
If  A = 
45
34
 
B= 
4-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 11 Answer: 8
Answer: 1 Answer: 1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
45
34
 
B= 
4-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
45
34
 
4-1
-11
 
= 
16+-5-4+5
12+-4-3+4
 
= 
111
81
 

 

(AB)T = 
118
11
 
.............(1)

To Find BTAT

BT = 
4-1
-11
 
AT = 
43
54
 

 

BTAT=
4-1
-11
 
43
54
 
= 
16-512-4
-4+5-3+4
 
= 
118
11
 
.......(2)

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

 



10)  
If  A = 
35
65
 
B= 
5-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 20
Answer: 14 Answer: 8
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
65
 
B= 
5-2
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
65
 
5-2
-24
 
= 
15+-10-6+20
30+-10-12+20
 
= 
514
208
 

 

(AB)T = 
520
148
 
.............(1)

To Find BTAT

BT = 
5-2
-24
 
AT = 
36
55
 

 

BTAT=
5-2
-24
 
36
55
 
= 
15-1030-10
-6+20-12+20
 
= 
520
148
 
.......(2)

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