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
45
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




2)  
If  A = 
54
65
 
B= 
6-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




3)  
If  A = 
54
33
 
B= 
6-3
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




4)  
If  A = 
32
54
 
B= 
6-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




5)  
If  A = 
42
63
 
B= 
4-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




6)  
If  A = 
54
75
 
B= 
6-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




7)  
If  A = 
43
74
 
B= 
4-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




8)  
If  A = 
22
75
 
B= 
4-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




9)  
If  A = 
53
54
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




10)  
If  A = 
54
53
 
B= 
5-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
 
 






Answer:_______________




 

1)  
If  A = 
43
45
 
B= 
6-2
-23
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 18 Answer: 14
Answer: 1 Answer: 7
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
45
 
B= 
6-2
-23
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
45
 
6-2
-23
 
= 
24+-6-8+9
24+-10-8+15
 
= 
181
147
 

 

(AB)T = 
1814
17
 
.............(1)

To Find BTAT

BT = 
6-2
-23
 
AT = 
44
35
 

 

BTAT=
6-2
-23
 
44
35
 
= 
24-624-10
-8+9-8+15
 
= 
1814
17
 
.......(2)

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

 



2)  
If  A = 
54
65
 
B= 
6-2
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 26 Answer: 31
Answer: 2 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
65
 
B= 
6-2
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
65
 
6-2
-13
 
= 
30+-4-10+12
36+-5-12+15
 
= 
262
313
 

 

(AB)T = 
2631
23
 
.............(1)

To Find BTAT

BT = 
6-1
-23
 
AT = 
56
45
 

 

BTAT=
6-1
-23
 
56
45
 
= 
30-436-5
-10+12-12+15
 
= 
2631
23
 
.......(2)

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

 



3)  
If  A = 
54
33
 
B= 
6-3
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 26 Answer: 15
Answer: -3 Answer: 0
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
33
 
B= 
6-3
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
33
 
6-3
-13
 
= 
30+-4-15+12
18+-3-9+9
 
= 
26-3
150
 

 

(AB)T = 
2615
-30
 
.............(1)

To Find BTAT

BT = 
6-1
-33
 
AT = 
53
43
 

 

BTAT=
6-1
-33
 
53
43
 
= 
30-418-3
-15+12-9+9
 
= 
2615
-30
 
.......(2)

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

 



4)  
If  A = 
32
54
 
B= 
6-3
-14
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 16 Answer: 26
Answer: -1 Answer: 1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
32
54
 
B= 
6-3
-14
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
32
54
 
6-3
-14
 
= 
18+-2-9+8
30+-4-15+16
 
= 
16-1
261
 

 

(AB)T = 
1626
-11
 
.............(1)

To Find BTAT

BT = 
6-1
-34
 
AT = 
35
24
 

 

BTAT=
6-1
-34
 
35
24
 
= 
18-230-4
-9+8-15+16
 
= 
1626
-11
 
.......(2)

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

 



5)  
If  A = 
42
63
 
B= 
4-3
-21
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 12 Answer: 18
Answer: -10 Answer: -15
 
 






SOLUTION 1 :

 Given:

 

If  A = 
42
63
 
B= 
4-3
-21
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
42
63
 
4-3
-21
 
= 
16+-4-12+2
24+-6-18+3
 
= 
12-10
18-15
 

 

(AB)T = 
1218
-10-15
 
.............(1)

To Find BTAT

BT = 
4-2
-31
 
AT = 
46
23
 

 

BTAT=
4-2
-31
 
46
23
 
= 
16-424-6
-12+2-18+3
 
= 
1218
-10-15
 
.......(2)

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

 



6)  
If  A = 
54
75
 
B= 
6-3
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 22 Answer: 32
Answer: 1 Answer: -1
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
75
 
B= 
6-3
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
75
 
6-3
-24
 
= 
30+-8-15+16
42+-10-21+20
 
= 
221
32-1
 

 

(AB)T = 
2232
1-1
 
.............(1)

To Find BTAT

BT = 
6-2
-34
 
AT = 
57
45
 

 

BTAT=
6-2
-34
 
57
45
 
= 
30-842-10
-15+16-21+20
 
= 
2232
1-1
 
.......(2)

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

 



7)  
If  A = 
43
74
 
B= 
4-1
-13
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 13 Answer: 24
Answer: 5 Answer: 5
 
 






SOLUTION 1 :

 Given:

 

If  A = 
43
74
 
B= 
4-1
-13
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
43
74
 
4-1
-13
 
= 
16+-3-4+9
28+-4-7+12
 
= 
135
245
 

 

(AB)T = 
1324
55
 
.............(1)

To Find BTAT

BT = 
4-1
-13
 
AT = 
47
34
 

 

BTAT=
4-1
-13
 
47
34
 
= 
16-328-4
-4+9-7+12
 
= 
1324
55
 
.......(2)

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

 



8)  
If  A = 
22
75
 
B= 
4-1
-22
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 4 Answer: 18
Answer: 2 Answer: 3
 
 






SOLUTION 1 :

 Given:

 

If  A = 
22
75
 
B= 
4-1
-22
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
22
75
 
4-1
-22
 
= 
8+-4-2+4
28+-10-7+10
 
= 
42
183
 

 

(AB)T = 
418
23
 
.............(1)

To Find BTAT

BT = 
4-2
-12
 
AT = 
27
25
 

 

BTAT=
4-2
-12
 
27
25
 
= 
8-428-10
-2+4-7+10
 
= 
418
23
 
.......(2)

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

 



9)  
If  A = 
53
54
 
B= 
6-3
-12
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 27 Answer: 26
Answer: -9 Answer: -7
 
 






SOLUTION 1 :

 Given:

 

If  A = 
53
54
 
B= 
6-3
-12
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
53
54
 
6-3
-12
 
= 
30+-3-15+6
30+-4-15+8
 
= 
27-9
26-7
 

 

(AB)T = 
2726
-9-7
 
.............(1)

To Find BTAT

BT = 
6-1
-32
 
AT = 
55
34
 

 

BTAT=
6-1
-32
 
55
34
 
= 
30-330-4
-15+6-15+8
 
= 
2726
-9-7
 
.......(2)

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

 



10)  
If  A = 
54
53
 
B= 
5-2
-24
 
verify that  (AB)= BTAT.

BTAT =

 
Answer: 17 Answer: 19
Answer: 6 Answer: 2
 
 






SOLUTION 1 :

 Given:

 

If  A = 
54
53
 
B= 
5-2
-24
 
verify that (AB)T = BTAT.

T0 find (AB)T

AB =
54
53
 
5-2
-24
 
= 
25+-8-10+16
25+-6-10+12
 
= 
176
192
 

 

(AB)T = 
1719
62
 
.............(1)

To Find BTAT

BT = 
5-2
-24
 
AT = 
55
43
 

 

BTAT=
5-2
-24
 
55
43
 
= 
25-825-6
-10+16-10+12
 
= 
1719
62
 
.......(2)

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