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
64
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
32
52
 
B= 
5-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
44
74
 
B= 
4-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
32
63
 
B= 
5-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
35
65
 
B= 
5-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
53
63
 
B= 
6-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
35
73
 
B= 
4-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
52
35
 
B= 
5-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
32
44
 
B= 
5-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
43
52
 
B= 
4-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
55
64
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 16
Answer: 15 Answer: 10
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
64
 
B= 
4-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
64
 
4-1
-24
 
= 
20+-10-5+20
24+-8-6+16
 
= 
1015
1610
 

 

(AB)T = 
1016
1510
 
.............(1)

To Find BTAT

BT = 
4-2
-14
 
AT = 
56
54
 

 

BTAT=
4-2
-14
 
56
54
 
= 
20-1024-8
-5+20-6+16
 
= 
1016
1510
 
.......(2)

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

 



2)  
If  A = 
32
52
 
B= 
5-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 13 Answer: 23
Answer: -2 Answer: -6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
52
 
B= 
5-2
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
52
 
5-2
-12
 
= 
15+-2-6+4
25+-2-10+4
 
= 
13-2
23-6
 

 

(AB)T = 
1323
-2-6
 
.............(1)

To Find BTAT

BT = 
5-1
-22
 
AT = 
35
22
 

 

BTAT=
5-1
-22
 
35
22
 
= 
15-225-2
-6+4-10+4
 
= 
1323
-2-6
 
.......(2)

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

 



3)  
If  A = 
44
74
 
B= 
4-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 24
Answer: 0 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
44
74
 
B= 
4-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
44
74
 
4-1
-11
 
= 
16+-4-4+4
28+-4-7+4
 
= 
120
24-3
 

 

(AB)T = 
1224
0-3
 
.............(1)

To Find BTAT

BT = 
4-1
-11
 
AT = 
47
44
 

 

BTAT=
4-1
-11
 
47
44
 
= 
16-428-4
-4+4-7+4
 
= 
1224
0-3
 
.......(2)

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

 



4)  
If  A = 
32
63
 
B= 
5-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 13 Answer: 27
Answer: 0 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
63
 
B= 
5-2
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
63
 
5-2
-13
 
= 
15+-2-6+6
30+-3-12+9
 
= 
130
27-3
 

 

(AB)T = 
1327
0-3
 
.............(1)

To Find BTAT

BT = 
5-1
-23
 
AT = 
36
23
 

 

BTAT=
5-1
-23
 
36
23
 
= 
15-230-3
-6+6-12+9
 
= 
1327
0-3
 
.......(2)

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

 



5)  
If  A = 
35
65
 
B= 
5-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 20
Answer: 11 Answer: 2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
65
 
B= 
5-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
65
 
5-3
-24
 
= 
15+-10-9+20
30+-10-18+20
 
= 
511
202
 

 

(AB)T = 
520
112
 
.............(1)

To Find BTAT

BT = 
5-2
-34
 
AT = 
36
55
 

 

BTAT=
5-2
-34
 
36
55
 
= 
15-1030-10
-9+20-18+20
 
= 
520
112
 
.......(2)

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

 



6)  
If  A = 
53
63
 
B= 
6-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 24 Answer: 30
Answer: 4 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
63
 
B= 
6-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
63
 
6-1
-23
 
= 
30+-6-5+9
36+-6-6+9
 
= 
244
303
 

 

(AB)T = 
2430
43
 
.............(1)

To Find BTAT

BT = 
6-2
-13
 
AT = 
56
33
 

 

BTAT=
6-2
-13
 
56
33
 
= 
30-636-6
-5+9-6+9
 
= 
2430
43
 
.......(2)

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

 



7)  
If  A = 
35
73
 
B= 
4-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 2 Answer: 22
Answer: -1 Answer: -11
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
73
 
B= 
4-2
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
73
 
4-2
-21
 
= 
12+-10-6+5
28+-6-14+3
 
= 
2-1
22-11
 

 

(AB)T = 
222
-1-11
 
.............(1)

To Find BTAT

BT = 
4-2
-21
 
AT = 
37
53
 

 

BTAT=
4-2
-21
 
37
53
 
= 
12-1028-6
-6+5-14+3
 
= 
222
-1-11
 
.......(2)

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

 



8)  
If  A = 
52
35
 
B= 
5-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 23 Answer: 10
Answer: -3 Answer: 2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
52
35
 
B= 
5-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
52
35
 
5-1
-11
 
= 
25+-2-5+2
15+-5-3+5
 
= 
23-3
102
 

 

(AB)T = 
2310
-32
 
.............(1)

To Find BTAT

BT = 
5-1
-11
 
AT = 
53
25
 

 

BTAT=
5-1
-11
 
53
25
 
= 
25-215-5
-5+2-3+5
 
= 
2310
-32
 
.......(2)

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

 



9)  
If  A = 
32
44
 
B= 
5-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 11 Answer: 12
Answer: -7 Answer: -8
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
44
 
B= 
5-3
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
44
 
5-3
-21
 
= 
15+-4-9+2
20+-8-12+4
 
= 
11-7
12-8
 

 

(AB)T = 
1112
-7-8
 
.............(1)

To Find BTAT

BT = 
5-2
-31
 
AT = 
34
24
 

 

BTAT=
5-2
-31
 
34
24
 
= 
15-420-8
-9+2-12+4
 
= 
1112
-7-8
 
.......(2)

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

 



10)  
If  A = 
43
52
 
B= 
4-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 16
Answer: -2 Answer: -6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
52
 
B= 
4-2
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
52
 
4-2
-22
 
= 
16+-6-8+6
20+-4-10+4
 
= 
10-2
16-6
 

 

(AB)T = 
1016
-2-6
 
.............(1)

To Find BTAT

BT = 
4-2
-22
 
AT = 
45
32
 

 

BTAT=
4-2
-22
 
45
32
 
= 
16-620-4
-8+6-10+4
 
= 
1016
-2-6
 
.......(2)

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