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 = 
24
54
 
B= 
5-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
35
33
 
B= 
5-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
54
64
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
44
33
 
B= 
6-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
25
63
 
B= 
4-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
35
42
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
23
33
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
53
64
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
55
53
 
B= 
5-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
54
52
 
B= 
4-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
24
54
 
B= 
5-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 2 Answer: 17
Answer: 14 Answer: 11
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
54
 
B= 
5-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
54
 
5-1
-24
 
= 
10+-8-2+16
25+-8-5+16
 
= 
214
1711
 

 

(AB)T = 
217
1411
 
.............(1)

To Find BTAT

BT = 
5-2
-14
 
AT = 
25
44
 

 

BTAT=
5-2
-14
 
25
44
 
= 
10-825-8
-2+16-5+16
 
= 
217
1411
 
.......(2)

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

 



2)  
If  A = 
35
33
 
B= 
5-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 9
Answer: 7 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
33
 
B= 
5-1
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
33
 
5-1
-22
 
= 
15+-10-3+10
15+-6-3+6
 
= 
57
93
 

 

(AB)T = 
59
73
 
.............(1)

To Find BTAT

BT = 
5-2
-12
 
AT = 
33
53
 

 

BTAT=
5-2
-12
 
33
53
 
= 
15-1015-6
-3+10-3+6
 
= 
59
73
 
.......(2)

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

 



3)  
If  A = 
54
64
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 22 Answer: 28
Answer: 2 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
64
 
B= 
6-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
64
 
6-2
-23
 
= 
30+-8-10+12
36+-8-12+12
 
= 
222
280
 

 

(AB)T = 
2228
20
 
.............(1)

To Find BTAT

BT = 
6-2
-23
 
AT = 
56
44
 

 

BTAT=
6-2
-23
 
56
44
 
= 
30-836-8
-10+12-12+12
 
= 
2228
20
 
.......(2)

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

 



4)  
If  A = 
44
33
 
B= 
6-2
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 16 Answer: 12
Answer: -4 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
44
33
 
B= 
6-2
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
44
33
 
6-2
-21
 
= 
24+-8-8+4
18+-6-6+3
 
= 
16-4
12-3
 

 

(AB)T = 
1612
-4-3
 
.............(1)

To Find BTAT

BT = 
6-2
-21
 
AT = 
43
43
 

 

BTAT=
6-2
-21
 
43
43
 
= 
24-818-6
-8+4-6+3
 
= 
1612
-4-3
 
.......(2)

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

 



5)  
If  A = 
25
63
 
B= 
4-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: -2 Answer: 18
Answer: 13 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
63
 
B= 
4-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
63
 
4-1
-23
 
= 
8+-10-2+15
24+-6-6+9
 
= 
-213
183
 

 

(AB)T = 
-218
133
 
.............(1)

To Find BTAT

BT = 
4-2
-13
 
AT = 
26
53
 

 

BTAT=
4-2
-13
 
26
53
 
= 
8-1024-6
-2+15-6+9
 
= 
-218
133
 
.......(2)

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

 



6)  
If  A = 
35
42
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 5 Answer: 16
Answer: 4 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
42
 
B= 
5-2
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
42
 
5-2
-22
 
= 
15+-10-6+10
20+-4-8+4
 
= 
54
16-4
 

 

(AB)T = 
516
4-4
 
.............(1)

To Find BTAT

BT = 
5-2
-22
 
AT = 
34
52
 

 

BTAT=
5-2
-22
 
34
52
 
= 
15-1020-4
-6+10-8+4
 
= 
516
4-4
 
.......(2)

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

 



7)  
If  A = 
23
33
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 9 Answer: 15
Answer: 0 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
23
33
 
B= 
6-3
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
23
33
 
6-3
-12
 
= 
12+-3-6+6
18+-3-9+6
 
= 
90
15-3
 

 

(AB)T = 
915
0-3
 
.............(1)

To Find BTAT

BT = 
6-1
-32
 
AT = 
23
33
 

 

BTAT=
6-1
-32
 
23
33
 
= 
12-318-3
-6+6-9+6
 
= 
915
0-3
 
.......(2)

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

 



8)  
If  A = 
53
64
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 27 Answer: 32
Answer: -2 Answer: -2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
64
 
B= 
6-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
64
 
6-1
-11
 
= 
30+-3-5+3
36+-4-6+4
 
= 
27-2
32-2
 

 

(AB)T = 
2732
-2-2
 
.............(1)

To Find BTAT

BT = 
6-1
-11
 
AT = 
56
34
 

 

BTAT=
6-1
-11
 
56
34
 
= 
30-336-4
-5+3-6+4
 
= 
2732
-2-2
 
.......(2)

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

 



9)  
If  A = 
55
53
 
B= 
5-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 20 Answer: 22
Answer: 0 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
53
 
B= 
5-2
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
53
 
5-2
-12
 
= 
25+-5-10+10
25+-3-10+6
 
= 
200
22-4
 

 

(AB)T = 
2022
0-4
 
.............(1)

To Find BTAT

BT = 
5-1
-22
 
AT = 
55
53
 

 

BTAT=
5-1
-22
 
55
53
 
= 
25-525-3
-10+10-10+6
 
= 
2022
0-4
 
.......(2)

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

 



10)  
If  A = 
54
52
 
B= 
4-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 16
Answer: -11 Answer: -13
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
52
 
B= 
4-3
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
52
 
4-3
-21
 
= 
20+-8-15+4
20+-4-15+2
 
= 
12-11
16-13
 

 

(AB)T = 
1216
-11-13
 
.............(1)

To Find BTAT

BT = 
4-2
-31
 
AT = 
55
42
 

 

BTAT=
4-2
-31
 
55
42
 
= 
20-820-4
-15+4-15+2
 
= 
1216
-11-13
 
.......(2)

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