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 = 
54
63
 
B= 
4-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
42
75
 
B= 
5-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
45
64
 
B= 
5-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
43
34
 
B= 
4-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
24
64
 
B= 
6-2
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
25
75
 
B= 
4-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
42
63
 
B= 
5-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
43
34
 
B= 
6-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
53
63
 
B= 
6-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
34
33
 
B= 
6-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
54
63
 
B= 
4-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 18
Answer: 2 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
63
 
B= 
4-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
63
 
4-2
-23
 
= 
20+-8-10+12
24+-6-12+9
 
= 
122
18-3
 

 

(AB)T = 
1218
2-3
 
.............(1)

To Find BTAT

BT = 
4-2
-23
 
AT = 
56
43
 

 

BTAT=
4-2
-23
 
56
43
 
= 
20-824-6
-10+12-12+9
 
= 
1218
2-3
 
.......(2)

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

 



2)  
If  A = 
42
75
 
B= 
5-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 18 Answer: 30
Answer: 2 Answer: 8
 
 






SOLUTION 1 :

 Given:

 

If  A = 
42
75
 
B= 
5-1
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
42
75
 
5-1
-13
 
= 
20+-2-4+6
35+-5-7+15
 
= 
182
308
 

 

(AB)T = 
1830
28
 
.............(1)

To Find BTAT

BT = 
5-1
-13
 
AT = 
47
25
 

 

BTAT=
5-1
-13
 
47
25
 
= 
20-235-5
-4+6-7+15
 
= 
1830
28
 
.......(2)

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

 



3)  
If  A = 
45
64
 
B= 
5-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 22
Answer: -2 Answer: -10
 
 






SOLUTION 1 :

 Given:

 

If  A = 
45
64
 
B= 
5-3
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
45
64
 
5-3
-22
 
= 
20+-10-12+10
30+-8-18+8
 
= 
10-2
22-10
 

 

(AB)T = 
1022
-2-10
 
.............(1)

To Find BTAT

BT = 
5-2
-32
 
AT = 
46
54
 

 

BTAT=
5-2
-32
 
46
54
 
= 
20-1030-8
-12+10-18+8
 
= 
1022
-2-10
 
.......(2)

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

 



4)  
If  A = 
43
34
 
B= 
4-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 13 Answer: 8
Answer: 8 Answer: 13
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
34
 
B= 
4-1
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
34
 
4-1
-14
 
= 
16+-3-4+12
12+-4-3+16
 
= 
138
813
 

 

(AB)T = 
138
813
 
.............(1)

To Find BTAT

BT = 
4-1
-14
 
AT = 
43
34
 

 

BTAT=
4-1
-14
 
43
34
 
= 
16-312-4
-4+12-3+16
 
= 
138
813
 
.......(2)

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

 



5)  
If  A = 
24
64
 
B= 
6-2
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 32
Answer: 12 Answer: 4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
64
 
B= 
6-2
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
64
 
6-2
-14
 
= 
12+-4-4+16
36+-4-12+16
 
= 
812
324
 

 

(AB)T = 
832
124
 
.............(1)

To Find BTAT

BT = 
6-1
-24
 
AT = 
26
44
 

 

BTAT=
6-1
-24
 
26
44
 
= 
12-436-4
-4+16-12+16
 
= 
832
124
 
.......(2)

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

 



6)  
If  A = 
25
75
 
B= 
4-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 3 Answer: 23
Answer: 4 Answer: -11
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
75
 
B= 
4-3
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
75
 
4-3
-12
 
= 
8+-5-6+10
28+-5-21+10
 
= 
34
23-11
 

 

(AB)T = 
323
4-11
 
.............(1)

To Find BTAT

BT = 
4-1
-32
 
AT = 
27
55
 

 

BTAT=
4-1
-32
 
27
55
 
= 
8-528-5
-6+10-21+10
 
= 
323
4-11
 
.......(2)

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

 



7)  
If  A = 
42
63
 
B= 
5-3
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 18 Answer: 27
Answer: -10 Answer: -15
 
 






SOLUTION 1 :

 Given:

 

If  A = 
42
63
 
B= 
5-3
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
42
63
 
5-3
-11
 
= 
20+-2-12+2
30+-3-18+3
 
= 
18-10
27-15
 

 

(AB)T = 
1827
-10-15
 
.............(1)

To Find BTAT

BT = 
5-1
-31
 
AT = 
46
23
 

 

BTAT=
5-1
-31
 
46
23
 
= 
20-230-3
-12+2-18+3
 
= 
1827
-10-15
 
.......(2)

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

 



8)  
If  A = 
43
34
 
B= 
6-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 21 Answer: 14
Answer: -2 Answer: 2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
34
 
B= 
6-2
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
34
 
6-2
-12
 
= 
24+-3-8+6
18+-4-6+8
 
= 
21-2
142
 

 

(AB)T = 
2114
-22
 
.............(1)

To Find BTAT

BT = 
6-1
-22
 
AT = 
43
34
 

 

BTAT=
6-1
-22
 
43
34
 
= 
24-318-4
-8+6-6+8
 
= 
2114
-22
 
.......(2)

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

 



9)  
If  A = 
53
63
 
B= 
6-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 24 Answer: 30
Answer: -3 Answer: -6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
63
 
B= 
6-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
63
 
6-3
-24
 
= 
30+-6-15+12
36+-6-18+12
 
= 
24-3
30-6
 

 

(AB)T = 
2430
-3-6
 
.............(1)

To Find BTAT

BT = 
6-2
-34
 
AT = 
56
33
 

 

BTAT=
6-2
-34
 
56
33
 
= 
30-636-6
-15+12-18+12
 
= 
2430
-3-6
 
.......(2)

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

 



10)  
If  A = 
34
33
 
B= 
6-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 15
Answer: 13 Answer: 9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
34
33
 
B= 
6-1
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
34
33
 
6-1
-14
 
= 
18+-4-3+16
18+-3-3+12
 
= 
1413
159
 

 

(AB)T = 
1415
139
 
.............(1)

To Find BTAT

BT = 
6-1
-14
 
AT = 
33
43
 

 

BTAT=
6-1
-14
 
33
43
 
= 
18-418-3
-3+16-3+12
 
= 
1415
139
 
.......(2)

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