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
54
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
55
42
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
55
42
 
B= 
5-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
24
65
 
B= 
4-3
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
25
35
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
54
53
 
B= 
4-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
45
64
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
55
35
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
35
32
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
24
53
 
B= 
6-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
54
54
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 17 Answer: 17
Answer: -2 Answer: -2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
54
 
B= 
5-2
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
54
 
5-2
-22
 
= 
25+-8-10+8
25+-8-10+8
 
= 
17-2
17-2
 

 

(AB)T = 
1717
-2-2
 
.............(1)

To Find BTAT

BT = 
5-2
-22
 
AT = 
55
44
 

 

BTAT=
5-2
-22
 
55
44
 
= 
25-825-8
-10+8-10+8
 
= 
1717
-2-2
 
.......(2)

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

 



2)  
If  A = 
55
42
 
B= 
4-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 15 Answer: 14
Answer: 5 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
42
 
B= 
4-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
42
 
4-1
-12
 
= 
20+-5-5+10
16+-2-4+4
 
= 
155
140
 

 

(AB)T = 
1514
50
 
.............(1)

To Find BTAT

BT = 
4-1
-12
 
AT = 
54
52
 

 

BTAT=
4-1
-12
 
54
52
 
= 
20-516-2
-5+10-4+4
 
= 
1514
50
 
.......(2)

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

 



3)  
If  A = 
55
42
 
B= 
5-1
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 20 Answer: 18
Answer: 5 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
42
 
B= 
5-1
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
42
 
5-1
-12
 
= 
25+-5-5+10
20+-2-4+4
 
= 
205
180
 

 

(AB)T = 
2018
50
 
.............(1)

To Find BTAT

BT = 
5-1
-12
 
AT = 
54
52
 

 

BTAT=
5-1
-12
 
54
52
 
= 
25-520-2
-5+10-4+4
 
= 
2018
50
 
.......(2)

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

 



4)  
If  A = 
24
65
 
B= 
4-3
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 0 Answer: 14
Answer: 6 Answer: -3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
65
 
B= 
4-3
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
65
 
4-3
-23
 
= 
8+-8-6+12
24+-10-18+15
 
= 
06
14-3
 

 

(AB)T = 
014
6-3
 
.............(1)

To Find BTAT

BT = 
4-2
-33
 
AT = 
26
45
 

 

BTAT=
4-2
-33
 
26
45
 
= 
8-824-10
-6+12-18+15
 
= 
014
6-3
 
.......(2)

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

 



5)  
If  A = 
25
35
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 0 Answer: 5
Answer: 13 Answer: 12
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
35
 
B= 
5-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
35
 
5-1
-23
 
= 
10+-10-2+15
15+-10-3+15
 
= 
013
512
 

 

(AB)T = 
05
1312
 
.............(1)

To Find BTAT

BT = 
5-2
-13
 
AT = 
23
55
 

 

BTAT=
5-2
-13
 
23
55
 
= 
10-1015-10
-2+15-3+15
 
= 
05
1312
 
.......(2)

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

 



6)  
If  A = 
54
53
 
B= 
4-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 16 Answer: 17
Answer: 2 Answer: -1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
53
 
B= 
4-2
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
53
 
4-2
-13
 
= 
20+-4-10+12
20+-3-10+9
 
= 
162
17-1
 

 

(AB)T = 
1617
2-1
 
.............(1)

To Find BTAT

BT = 
4-1
-23
 
AT = 
55
43
 

 

BTAT=
4-1
-23
 
55
43
 
= 
20-420-3
-10+12-10+9
 
= 
1617
2-1
 
.......(2)

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

 



7)  
If  A = 
45
64
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 16
Answer: 16 Answer: 10
 
 






SOLUTION 1 :

 Given:

 

If  A = 
45
64
 
B= 
4-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
45
64
 
4-1
-24
 
= 
16+-10-4+20
24+-8-6+16
 
= 
616
1610
 

 

(AB)T = 
616
1610
 
.............(1)

To Find BTAT

BT = 
4-2
-14
 
AT = 
46
54
 

 

BTAT=
4-2
-14
 
46
54
 
= 
16-1024-8
-4+20-6+16
 
= 
616
1610
 
.......(2)

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

 



8)  
If  A = 
55
35
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 25 Answer: 13
Answer: 0 Answer: 2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
35
 
B= 
6-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
35
 
6-1
-11
 
= 
30+-5-5+5
18+-5-3+5
 
= 
250
132
 

 

(AB)T = 
2513
02
 
.............(1)

To Find BTAT

BT = 
6-1
-11
 
AT = 
53
55
 

 

BTAT=
6-1
-11
 
53
55
 
= 
30-518-5
-5+5-3+5
 
= 
2513
02
 
.......(2)

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

 



9)  
If  A = 
35
32
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 8 Answer: 14
Answer: 9 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
35
32
 
B= 
6-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
35
32
 
6-2
-23
 
= 
18+-10-6+15
18+-4-6+6
 
= 
89
140
 

 

(AB)T = 
814
90
 
.............(1)

To Find BTAT

BT = 
6-2
-23
 
AT = 
33
52
 

 

BTAT=
6-2
-23
 
33
52
 
= 
18-1018-4
-6+15-6+6
 
= 
814
90
 
.......(2)

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

 



10)  
If  A = 
24
53
 
B= 
6-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 4 Answer: 24
Answer: 2 Answer: -9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
53
 
B= 
6-3
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
53
 
6-3
-22
 
= 
12+-8-6+8
30+-6-15+6
 
= 
42
24-9
 

 

(AB)T = 
424
2-9
 
.............(1)

To Find BTAT

BT = 
6-2
-32
 
AT = 
25
43
 

 

BTAT=
6-2
-32
 
25
43
 
= 
12-830-6
-6+8-15+6
 
= 
424
2-9
 
.......(2)

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