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 = 
43
55
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
52
72
 
B= 
6-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
55
33
 
B= 
4-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
42
72
 
B= 
4-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
52
52
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
52
53
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
43
42
 
B= 
5-3
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
22
74
 
B= 
5-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
32
45
 
B= 
6-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
22
43
 
B= 
5-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
43
55
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 13 Answer: 15
Answer: 2 Answer: 5
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
55
 
B= 
4-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
55
 
4-1
-12
 
= 
16+-3-4+6
20+-5-5+10
 
= 
132
155
 

 

(AB)T = 
1315
25
 
.............(1)

To Find BTAT

BT = 
4-1
-12
 
AT = 
45
35
 

 

BTAT=
4-1
-12
 
45
35
 
= 
16-320-5
-4+6-5+10
 
= 
1315
25
 
.......(2)

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

 



2)  
If  A = 
52
72
 
B= 
6-2
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 28 Answer: 40
Answer: -6 Answer: -10
 
 






SOLUTION 1 :

 Given:

 

If  A = 
52
72
 
B= 
6-2
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
52
72
 
6-2
-12
 
= 
30+-2-10+4
42+-2-14+4
 
= 
28-6
40-10
 

 

(AB)T = 
2840
-6-10
 
.............(1)

To Find BTAT

BT = 
6-1
-22
 
AT = 
57
22
 

 

BTAT=
6-1
-22
 
57
22
 
= 
30-242-2
-10+4-14+4
 
= 
2840
-6-10
 
.......(2)

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

 



3)  
If  A = 
55
33
 
B= 
4-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 15 Answer: 9
Answer: 15 Answer: 9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
33
 
B= 
4-1
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
33
 
4-1
-14
 
= 
20+-5-5+20
12+-3-3+12
 
= 
1515
99
 

 

(AB)T = 
159
159
 
.............(1)

To Find BTAT

BT = 
4-1
-14
 
AT = 
53
53
 

 

BTAT=
4-1
-14
 
53
53
 
= 
20-512-3
-5+20-3+12
 
= 
159
159
 
.......(2)

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

 



4)  
If  A = 
42
72
 
B= 
4-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 26
Answer: -4 Answer: -13
 
 






SOLUTION 1 :

 Given:

 

If  A = 
42
72
 
B= 
4-3
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
42
72
 
4-3
-14
 
= 
16+-2-12+8
28+-2-21+8
 
= 
14-4
26-13
 

 

(AB)T = 
1426
-4-13
 
.............(1)

To Find BTAT

BT = 
4-1
-34
 
AT = 
47
22
 

 

BTAT=
4-1
-34
 
47
22
 
= 
16-228-2
-12+8-21+8
 
= 
1426
-4-13
 
.......(2)

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

 



5)  
If  A = 
52
52
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 16 Answer: 16
Answer: 3 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
52
52
 
B= 
4-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
52
52
 
4-1
-24
 
= 
20+-4-5+8
20+-4-5+8
 
= 
163
163
 

 

(AB)T = 
1616
33
 
.............(1)

To Find BTAT

BT = 
4-2
-14
 
AT = 
55
22
 

 

BTAT=
4-2
-14
 
55
22
 
= 
20-420-4
-5+8-5+8
 
= 
1616
33
 
.......(2)

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

 



6)  
If  A = 
52
53
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 21 Answer: 19
Answer: -6 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
52
53
 
B= 
5-2
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
52
53
 
5-2
-22
 
= 
25+-4-10+4
25+-6-10+6
 
= 
21-6
19-4
 

 

(AB)T = 
2119
-6-4
 
.............(1)

To Find BTAT

BT = 
5-2
-22
 
AT = 
55
23
 

 

BTAT=
5-2
-22
 
55
23
 
= 
25-425-6
-10+4-10+6
 
= 
2119
-6-4
 
.......(2)

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

 



7)  
If  A = 
43
42
 
B= 
5-3
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 17 Answer: 18
Answer: -3 Answer: -6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
42
 
B= 
5-3
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
42
 
5-3
-13
 
= 
20+-3-12+9
20+-2-12+6
 
= 
17-3
18-6
 

 

(AB)T = 
1718
-3-6
 
.............(1)

To Find BTAT

BT = 
5-1
-33
 
AT = 
44
32
 

 

BTAT=
5-1
-33
 
44
32
 
= 
20-320-2
-12+9-12+6
 
= 
1718
-3-6
 
.......(2)

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

 



8)  
If  A = 
22
74
 
B= 
5-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 27
Answer: 6 Answer: 9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
74
 
B= 
5-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
74
 
5-1
-24
 
= 
10+-4-2+8
35+-8-7+16
 
= 
66
279
 

 

(AB)T = 
627
69
 
.............(1)

To Find BTAT

BT = 
5-2
-14
 
AT = 
27
24
 

 

BTAT=
5-2
-14
 
27
24
 
= 
10-435-8
-2+8-7+16
 
= 
627
69
 
.......(2)

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

 



9)  
If  A = 
32
45
 
B= 
6-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 14
Answer: 5 Answer: 16
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
45
 
B= 
6-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
45
 
6-1
-24
 
= 
18+-4-3+8
24+-10-4+20
 
= 
145
1416
 

 

(AB)T = 
1414
516
 
.............(1)

To Find BTAT

BT = 
6-2
-14
 
AT = 
34
25
 

 

BTAT=
6-2
-14
 
34
25
 
= 
18-424-10
-3+8-4+20
 
= 
1414
516
 
.......(2)

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

 



10)  
If  A = 
22
43
 
B= 
5-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 17
Answer: 4 Answer: 5
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
43
 
B= 
5-1
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
43
 
5-1
-13
 
= 
10+-2-2+6
20+-3-4+9
 
= 
84
175
 

 

(AB)T = 
817
45
 
.............(1)

To Find BTAT

BT = 
5-1
-13
 
AT = 
24
23
 

 

BTAT=
5-1
-13
 
24
23
 
= 
10-220-3
-2+6-4+9
 
= 
817
45
 
.......(2)

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