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 = 
34
62
 
B= 
6-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
22
63
 
B= 
5-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
25
34
 
B= 
4-2
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
53
64
 
B= 
6-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
33
45
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
25
34
 
B= 
4-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
42
44
 
B= 
4-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
24
44
 
B= 
4-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
55
72
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
45
52
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
34
62
 
B= 
6-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 32
Answer: 9 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
34
62
 
B= 
6-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
34
62
 
6-1
-23
 
= 
18+-8-3+12
36+-4-6+6
 
= 
109
320
 

 

(AB)T = 
1032
90
 
.............(1)

To Find BTAT

BT = 
6-2
-13
 
AT = 
36
42
 

 

BTAT=
6-2
-13
 
36
42
 
= 
18-836-4
-3+12-6+6
 
= 
1032
90
 
.......(2)

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

 



2)  
If  A = 
22
63
 
B= 
5-3
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 6 Answer: 24
Answer: -2 Answer: -12
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
63
 
B= 
5-3
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
63
 
5-3
-22
 
= 
10+-4-6+4
30+-6-18+6
 
= 
6-2
24-12
 

 

(AB)T = 
624
-2-12
 
.............(1)

To Find BTAT

BT = 
5-2
-32
 
AT = 
26
23
 

 

BTAT=
5-2
-32
 
26
23
 
= 
10-430-6
-6+4-18+6
 
= 
624
-2-12
 
.......(2)

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

 



3)  
If  A = 
25
34
 
B= 
4-2
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 3 Answer: 8
Answer: 1 Answer: -2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
34
 
B= 
4-2
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
34
 
4-2
-11
 
= 
8+-5-4+5
12+-4-6+4
 
= 
31
8-2
 

 

(AB)T = 
38
1-2
 
.............(1)

To Find BTAT

BT = 
4-1
-21
 
AT = 
23
54
 

 

BTAT=
4-1
-21
 
23
54
 
= 
8-512-4
-4+5-6+4
 
= 
38
1-2
 
.......(2)

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

 



4)  
If  A = 
53
64
 
B= 
6-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 27 Answer: 32
Answer: 4 Answer: 6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
64
 
B= 
6-1
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
64
 
6-1
-13
 
= 
30+-3-5+9
36+-4-6+12
 
= 
274
326
 

 

(AB)T = 
2732
46
 
.............(1)

To Find BTAT

BT = 
6-1
-13
 
AT = 
56
34
 

 

BTAT=
6-1
-13
 
56
34
 
= 
30-336-4
-5+9-6+12
 
= 
2732
46
 
.......(2)

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

 



5)  
If  A = 
33
45
 
B= 
5-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 9 Answer: 10
Answer: 6 Answer: 11
 
 






SOLUTION 1 :

 Given:

 

If  A = 
33
45
 
B= 
5-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
33
45
 
5-1
-23
 
= 
15+-6-3+9
20+-10-4+15
 
= 
96
1011
 

 

(AB)T = 
910
611
 
.............(1)

To Find BTAT

BT = 
5-2
-13
 
AT = 
34
35
 

 

BTAT=
5-2
-13
 
34
35
 
= 
15-620-10
-3+9-4+15
 
= 
910
611
 
.......(2)

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

 



6)  
If  A = 
25
34
 
B= 
4-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: -2 Answer: 4
Answer: 13 Answer: 9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
25
34
 
B= 
4-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
25
34
 
4-1
-23
 
= 
8+-10-2+15
12+-8-3+12
 
= 
-213
49
 

 

(AB)T = 
-24
139
 
.............(1)

To Find BTAT

BT = 
4-2
-13
 
AT = 
23
54
 

 

BTAT=
4-2
-13
 
23
54
 
= 
8-1012-8
-2+15-3+12
 
= 
-24
139
 
.......(2)

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

 



7)  
If  A = 
42
44
 
B= 
4-1
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 12
Answer: 4 Answer: 12
 
 






SOLUTION 1 :

 Given:

 

If  A = 
42
44
 
B= 
4-1
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
42
44
 
4-1
-14
 
= 
16+-2-4+8
16+-4-4+16
 
= 
144
1212
 

 

(AB)T = 
1412
412
 
.............(1)

To Find BTAT

BT = 
4-1
-14
 
AT = 
44
24
 

 

BTAT=
4-1
-14
 
44
24
 
= 
16-216-4
-4+8-4+16
 
= 
1412
412
 
.......(2)

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

 



8)  
If  A = 
24
44
 
B= 
4-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 0 Answer: 8
Answer: 12 Answer: 8
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
44
 
B= 
4-2
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
44
 
4-2
-24
 
= 
8+-8-4+16
16+-8-8+16
 
= 
012
88
 

 

(AB)T = 
08
128
 
.............(1)

To Find BTAT

BT = 
4-2
-24
 
AT = 
24
44
 

 

BTAT=
4-2
-24
 
24
44
 
= 
8-816-8
-4+16-8+16
 
= 
08
128
 
.......(2)

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

 



9)  
If  A = 
55
72
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 15 Answer: 31
Answer: 0 Answer: -10
 
 






SOLUTION 1 :

 Given:

 

If  A = 
55
72
 
B= 
5-2
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
55
72
 
5-2
-22
 
= 
25+-10-10+10
35+-4-14+4
 
= 
150
31-10
 

 

(AB)T = 
1531
0-10
 
.............(1)

To Find BTAT

BT = 
5-2
-22
 
AT = 
57
52
 

 

BTAT=
5-2
-22
 
57
52
 
= 
25-1035-4
-10+10-14+4
 
= 
1531
0-10
 
.......(2)

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

 



10)  
If  A = 
45
52
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 26
Answer: 7 Answer: -4
 
 






SOLUTION 1 :

 Given:

 

If  A = 
45
52
 
B= 
6-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
45
52
 
6-2
-23
 
= 
24+-10-8+15
30+-4-10+6
 
= 
147
26-4
 

 

(AB)T = 
1426
7-4
 
.............(1)

To Find BTAT

BT = 
6-2
-23
 
AT = 
45
52
 

 

BTAT=
6-2
-23
 
45
52
 
= 
24-1030-4
-8+15-10+6
 
= 
1426
7-4
 
.......(2)

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