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
74
 
B= 
5-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
32
55
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
43
63
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
22
34
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
22
34
 
B= 
4-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
43
32
 
B= 
5-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
24
43
 
B= 
5-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
52
43
 
B= 
6-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
52
45
 
B= 
6-2
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
43
33
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
34
74
 
B= 
5-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 7 Answer: 27
Answer: 7 Answer: -5
 
 






SOLUTION 1 :

 Given:

 

If  A = 
34
74
 
B= 
5-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
34
74
 
5-3
-24
 
= 
15+-8-9+16
35+-8-21+16
 
= 
77
27-5
 

 

(AB)T = 
727
7-5
 
.............(1)

To Find BTAT

BT = 
5-2
-34
 
AT = 
37
44
 

 

BTAT=
5-2
-34
 
37
44
 
= 
15-835-8
-9+16-21+16
 
= 
727
7-5
 
.......(2)

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

 



2)  
If  A = 
32
55
 
B= 
5-2
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 11 Answer: 15
Answer: -2 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
55
 
B= 
5-2
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
55
 
5-2
-22
 
= 
15+-4-6+4
25+-10-10+10
 
= 
11-2
150
 

 

(AB)T = 
1115
-20
 
.............(1)

To Find BTAT

BT = 
5-2
-22
 
AT = 
35
25
 

 

BTAT=
5-2
-22
 
35
25
 
= 
15-425-10
-6+4-10+10
 
= 
1115
-20
 
.......(2)

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

 



3)  
If  A = 
43
63
 
B= 
4-1
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 18
Answer: 8 Answer: 6
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
63
 
B= 
4-1
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
63
 
4-1
-24
 
= 
16+-6-4+12
24+-6-6+12
 
= 
108
186
 

 

(AB)T = 
1018
86
 
.............(1)

To Find BTAT

BT = 
4-2
-14
 
AT = 
46
33
 

 

BTAT=
4-2
-14
 
46
33
 
= 
16-624-6
-4+12-6+12
 
= 
1018
86
 
.......(2)

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

 



4)  
If  A = 
22
34
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 10 Answer: 14
Answer: 0 Answer: 1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
34
 
B= 
6-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
34
 
6-1
-11
 
= 
12+-2-2+2
18+-4-3+4
 
= 
100
141
 

 

(AB)T = 
1014
01
 
.............(1)

To Find BTAT

BT = 
6-1
-11
 
AT = 
23
24
 

 

BTAT=
6-1
-11
 
23
24
 
= 
12-218-4
-2+2-3+4
 
= 
1014
01
 
.......(2)

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

 



5)  
If  A = 
22
34
 
B= 
4-1
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 4 Answer: 4
Answer: 4 Answer: 9
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
34
 
B= 
4-1
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
34
 
4-1
-23
 
= 
8+-4-2+6
12+-8-3+12
 
= 
44
49
 

 

(AB)T = 
44
49
 
.............(1)

To Find BTAT

BT = 
4-2
-13
 
AT = 
23
24
 

 

BTAT=
4-2
-13
 
23
24
 
= 
8-412-8
-2+6-3+12
 
= 
44
49
 
.......(2)

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

 



6)  
If  A = 
43
32
 
B= 
5-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 14 Answer: 11
Answer: -9 Answer: -7
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
32
 
B= 
5-3
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
32
 
5-3
-21
 
= 
20+-6-12+3
15+-4-9+2
 
= 
14-9
11-7
 

 

(AB)T = 
1411
-9-7
 
.............(1)

To Find BTAT

BT = 
5-2
-31
 
AT = 
43
32
 

 

BTAT=
5-2
-31
 
43
32
 
= 
20-615-4
-12+3-9+2
 
= 
1411
-9-7
 
.......(2)

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

 



7)  
If  A = 
24
43
 
B= 
5-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 2 Answer: 14
Answer: 6 Answer: 2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
24
43
 
B= 
5-1
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
24
43
 
5-1
-22
 
= 
10+-8-2+8
20+-6-4+6
 
= 
26
142
 

 

(AB)T = 
214
62
 
.............(1)

To Find BTAT

BT = 
5-2
-12
 
AT = 
24
43
 

 

BTAT=
5-2
-12
 
24
43
 
= 
10-820-6
-2+8-4+6
 
= 
214
62
 
.......(2)

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

 



8)  
If  A = 
52
43
 
B= 
6-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 28 Answer: 21
Answer: -7 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
52
43
 
B= 
6-3
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
52
43
 
6-3
-14
 
= 
30+-2-15+8
24+-3-12+12
 
= 
28-7
210
 

 

(AB)T = 
2821
-70
 
.............(1)

To Find BTAT

BT = 
6-1
-34
 
AT = 
54
23
 

 

BTAT=
6-1
-34
 
54
23
 
= 
30-224-3
-15+8-12+12
 
= 
2821
-70
 
.......(2)

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

 



9)  
If  A = 
52
45
 
B= 
6-2
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 28 Answer: 19
Answer: -2 Answer: 12
 
 






SOLUTION 1 :

 Given:

 

If  A = 
52
45
 
B= 
6-2
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
52
45
 
6-2
-14
 
= 
30+-2-10+8
24+-5-8+20
 
= 
28-2
1912
 

 

(AB)T = 
2819
-212
 
.............(1)

To Find BTAT

BT = 
6-1
-24
 
AT = 
54
25
 

 

BTAT=
6-1
-24
 
54
25
 
= 
30-224-5
-10+8-8+20
 
= 
2819
-212
 
.......(2)

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

 



10)  
If  A = 
43
33
 
B= 
6-1
-11
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 21 Answer: 15
Answer: -1 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
33
 
B= 
6-1
-11
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
33
 
6-1
-11
 
= 
24+-3-4+3
18+-3-3+3
 
= 
21-1
150
 

 

(AB)T = 
2115
-10
 
.............(1)

To Find BTAT

BT = 
6-1
-11
 
AT = 
43
33
 

 

BTAT=
6-1
-11
 
43
33
 
= 
24-318-3
-4+3-3+3
 
= 
2115
-10
 
.......(2)

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