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 Page 1


Topic: Matrices 
Question bank with solutions 
One mark question ( V S A) 
1. Define matrix  
2. Define a diagonal matrix  
3. Define scalar matrix 
4. Define symmetric matrix  
5. Define skew-symmetric matrix  
6.In a matrix       [
2 5 19  -17
35 -2
5
2
     12
v3 1 -5    17
]   
find  1) order of the matrix  
         2)  Write the elements of ?? 13
 ,?? 21
  , ?? 33
 , ?? 24
  , ?? 23
 
7. If a matrix 8 elements what is the possible order it can have ? 
8. If a matrix 18 elements  what is the possible order it can have? 
9. construct 2 × 2 matrix  [?? ????
]    whose elements are given by  
 1) ?? ????
 = (?? + ?? ) 
2
   2) ?? ????
 = 
(?? +?? ) 
2
2
  
10. construct the 2 × 3 matrix whose elements are given by   ?? ????
= |?? - ?? | 
11. Construct the 3× 2 matrix whose elements are given by   ?? ????
= 
?? ??   
12. Find x, y, z if  [
4 3
?? 5
]= [
?? ?? 1 5
]  
13. Find x, y, z if  [
?? + ?? 2
5 + ?? ????
]= [
6 2
5 8
]  
14. Find the  matrix x such that 2A + B + X =0 where A = [
-1 2
3 4
]  and B = [
3 -2
1 5
]  
15. If A = [
1 2 3
2 3 1
]     B =  [
3 -1 3
-1 0 2
]     Find 2A – B 
Page 2


Topic: Matrices 
Question bank with solutions 
One mark question ( V S A) 
1. Define matrix  
2. Define a diagonal matrix  
3. Define scalar matrix 
4. Define symmetric matrix  
5. Define skew-symmetric matrix  
6.In a matrix       [
2 5 19  -17
35 -2
5
2
     12
v3 1 -5    17
]   
find  1) order of the matrix  
         2)  Write the elements of ?? 13
 ,?? 21
  , ?? 33
 , ?? 24
  , ?? 23
 
7. If a matrix 8 elements what is the possible order it can have ? 
8. If a matrix 18 elements  what is the possible order it can have? 
9. construct 2 × 2 matrix  [?? ????
]    whose elements are given by  
 1) ?? ????
 = (?? + ?? ) 
2
   2) ?? ????
 = 
(?? +?? ) 
2
2
  
10. construct the 2 × 3 matrix whose elements are given by   ?? ????
= |?? - ?? | 
11. Construct the 3× 2 matrix whose elements are given by   ?? ????
= 
?? ??   
12. Find x, y, z if  [
4 3
?? 5
]= [
?? ?? 1 5
]  
13. Find x, y, z if  [
?? + ?? 2
5 + ?? ????
]= [
6 2
5 8
]  
14. Find the  matrix x such that 2A + B + X =0 where A = [
-1 2
3 4
]  and B = [
3 -2
1 5
]  
15. If A = [
1 2 3
2 3 1
]     B =  [
3 -1 3
-1 0 2
]     Find 2A – B 
16. Find X if Y =[
3 2
1 4
] and 2X+Y = [
1 0
-3 2
]  
17. Find X If  X+Y = [
7 0
2 5
] and X-Y = [
3 0
0 3
]  
18. Simplify   cos?? [
cos?? sin?? -sin?? cos?? ] + sin?? [
sin?? -cos?? cos?? sin?? ]  
19. Find X If  2[
1 3
0 ?? ] + [
?? 0
1 2
] = [
5 6
1 8
] 
20. If A = [
1 2
3 4
] Find A + ?? 1
  
21. A =  [
1 -2 3
0 1 4
]     and B = [
0 2 5
6 -3 1
]     Find 3A + 2B  
22. if  A = [
sin?? cos?? -cos?? sin?? ] Verify A A
1
 = I  
23. if B = [
cos?? sin?? -sin?? cos?? ] verify B B
1
= I 
24. If A = [
0
1
2
]  B = [
1 5 7
] Find AB 
25. Compute  1) [
1 -2
2 3
] [
1 2 3
2 3 1
]  
           2) [
3 -1 3
-1 0 2
][
2 -3
1 0
3 1
] 
26. Find X and Y [
2?? + ?? 3?? 6 4
]  =  [
6 0
6 4
] 
27. What is the number of possible square matrix order 3 with each entries 0 or 1  
28. Find X and Y if  [
5 - ?? 2?? - 8
0 3
] is a scalar matrix  
29. Find X   [
4 ?? + 2
2?? - 3 ?? + 1
] is a symmetric matrix  
  
Page 3


Topic: Matrices 
Question bank with solutions 
One mark question ( V S A) 
1. Define matrix  
2. Define a diagonal matrix  
3. Define scalar matrix 
4. Define symmetric matrix  
5. Define skew-symmetric matrix  
6.In a matrix       [
2 5 19  -17
35 -2
5
2
     12
v3 1 -5    17
]   
find  1) order of the matrix  
         2)  Write the elements of ?? 13
 ,?? 21
  , ?? 33
 , ?? 24
  , ?? 23
 
7. If a matrix 8 elements what is the possible order it can have ? 
8. If a matrix 18 elements  what is the possible order it can have? 
9. construct 2 × 2 matrix  [?? ????
]    whose elements are given by  
 1) ?? ????
 = (?? + ?? ) 
2
   2) ?? ????
 = 
(?? +?? ) 
2
2
  
10. construct the 2 × 3 matrix whose elements are given by   ?? ????
= |?? - ?? | 
11. Construct the 3× 2 matrix whose elements are given by   ?? ????
= 
?? ??   
12. Find x, y, z if  [
4 3
?? 5
]= [
?? ?? 1 5
]  
13. Find x, y, z if  [
?? + ?? 2
5 + ?? ????
]= [
6 2
5 8
]  
14. Find the  matrix x such that 2A + B + X =0 where A = [
-1 2
3 4
]  and B = [
3 -2
1 5
]  
15. If A = [
1 2 3
2 3 1
]     B =  [
3 -1 3
-1 0 2
]     Find 2A – B 
16. Find X if Y =[
3 2
1 4
] and 2X+Y = [
1 0
-3 2
]  
17. Find X If  X+Y = [
7 0
2 5
] and X-Y = [
3 0
0 3
]  
18. Simplify   cos?? [
cos?? sin?? -sin?? cos?? ] + sin?? [
sin?? -cos?? cos?? sin?? ]  
19. Find X If  2[
1 3
0 ?? ] + [
?? 0
1 2
] = [
5 6
1 8
] 
20. If A = [
1 2
3 4
] Find A + ?? 1
  
21. A =  [
1 -2 3
0 1 4
]     and B = [
0 2 5
6 -3 1
]     Find 3A + 2B  
22. if  A = [
sin?? cos?? -cos?? sin?? ] Verify A A
1
 = I  
23. if B = [
cos?? sin?? -sin?? cos?? ] verify B B
1
= I 
24. If A = [
0
1
2
]  B = [
1 5 7
] Find AB 
25. Compute  1) [
1 -2
2 3
] [
1 2 3
2 3 1
]  
           2) [
3 -1 3
-1 0 2
][
2 -3
1 0
3 1
] 
26. Find X and Y [
2?? + ?? 3?? 6 4
]  =  [
6 0
6 4
] 
27. What is the number of possible square matrix order 3 with each entries 0 or 1  
28. Find X and Y if  [
5 - ?? 2?? - 8
0 3
] is a scalar matrix  
29. Find X   [
4 ?? + 2
2?? - 3 ?? + 1
] is a symmetric matrix  
  
II. Two mark and Three  marks  questions (SA) 
1.Radha , fauzia, simran are the student of 12
th
 class Radha has 15 note book and 6 pens , 
Fauzia has  10 books 2 pens  and Simran has 13 books and 5 pens express this in to matrix 
forms.  
2. Construct 3× 2 matrix whose elements are given by    ?? ????
=
1
2
  |?? - 3?? | 
3. Find X,Y,Z from the equation [
?? + ?? + ?? ?? + ?? ?? + ?? ] = [
9
5
7
] 
4. Find a,b,c, d From the equation  [
?? - ?? 2?? + ?? 2?? - ?? 3?? + ?? ] = = [
-1 5
0 13
] 
5. If  A =  [
8 0
4 -2
3 6
]   B = [
2 -2
4 2
-5 1
] Find X  such that 2A + 3X = 5B 
6. Find X and Y 2[
?? 5
7 ?? - 3
] + [
3 -4
1 2
] = [
7 6
15 14
]  
7. Find X and Y  if x [
2
3
]+ ?? [
-1
1
]= [
10
5
]  
8. Given  3 [
?? ?? ?? ?? ] = [
?? 6
-1 2?? ] +  [
4 ?? + ?? ?? + ?? 3
] Fine the values  of X,Y,Z and W 
9. If ?? ?? = [
cos?? sin?? -sin?? cos?? ]  and ?? ?? =  [
cos?? sin?? -sin?? cos?? ]  Show that ?? ?? ?? ?? = ?? ?? +?? 
10. If A = [
3 -2
4 -2
] and I = [
1 0
0 1
] Find K If A
2
 = KA – 2I 
11. If A =  [
3 v3 2
4 2 0
] and B =[
2 -1 2
1 2 4
]  verify (A + B )
1
 = A
1
 +B
1
 
12. For any matrix A with real number entries , A+ A
1
 is symmetric matrix and A – A
1
 
Skew-symmetric matrix  
13. For any  matrix   A  = [
1 5
6 7
] verify that A+ A
1
 is symmetric matrix 
14. For any  matrix   A  = [
1 5
6 7
] verify that A – A
1
 Skew-symmetric matrix  
15. If A and B be the invertible matrices of same order  then (AB)
-1
 = B
-1
A
-1
 
16. By using elementary operation Find the inverse of the matrix [
1 2
2 -1
] 
Page 4


Topic: Matrices 
Question bank with solutions 
One mark question ( V S A) 
1. Define matrix  
2. Define a diagonal matrix  
3. Define scalar matrix 
4. Define symmetric matrix  
5. Define skew-symmetric matrix  
6.In a matrix       [
2 5 19  -17
35 -2
5
2
     12
v3 1 -5    17
]   
find  1) order of the matrix  
         2)  Write the elements of ?? 13
 ,?? 21
  , ?? 33
 , ?? 24
  , ?? 23
 
7. If a matrix 8 elements what is the possible order it can have ? 
8. If a matrix 18 elements  what is the possible order it can have? 
9. construct 2 × 2 matrix  [?? ????
]    whose elements are given by  
 1) ?? ????
 = (?? + ?? ) 
2
   2) ?? ????
 = 
(?? +?? ) 
2
2
  
10. construct the 2 × 3 matrix whose elements are given by   ?? ????
= |?? - ?? | 
11. Construct the 3× 2 matrix whose elements are given by   ?? ????
= 
?? ??   
12. Find x, y, z if  [
4 3
?? 5
]= [
?? ?? 1 5
]  
13. Find x, y, z if  [
?? + ?? 2
5 + ?? ????
]= [
6 2
5 8
]  
14. Find the  matrix x such that 2A + B + X =0 where A = [
-1 2
3 4
]  and B = [
3 -2
1 5
]  
15. If A = [
1 2 3
2 3 1
]     B =  [
3 -1 3
-1 0 2
]     Find 2A – B 
16. Find X if Y =[
3 2
1 4
] and 2X+Y = [
1 0
-3 2
]  
17. Find X If  X+Y = [
7 0
2 5
] and X-Y = [
3 0
0 3
]  
18. Simplify   cos?? [
cos?? sin?? -sin?? cos?? ] + sin?? [
sin?? -cos?? cos?? sin?? ]  
19. Find X If  2[
1 3
0 ?? ] + [
?? 0
1 2
] = [
5 6
1 8
] 
20. If A = [
1 2
3 4
] Find A + ?? 1
  
21. A =  [
1 -2 3
0 1 4
]     and B = [
0 2 5
6 -3 1
]     Find 3A + 2B  
22. if  A = [
sin?? cos?? -cos?? sin?? ] Verify A A
1
 = I  
23. if B = [
cos?? sin?? -sin?? cos?? ] verify B B
1
= I 
24. If A = [
0
1
2
]  B = [
1 5 7
] Find AB 
25. Compute  1) [
1 -2
2 3
] [
1 2 3
2 3 1
]  
           2) [
3 -1 3
-1 0 2
][
2 -3
1 0
3 1
] 
26. Find X and Y [
2?? + ?? 3?? 6 4
]  =  [
6 0
6 4
] 
27. What is the number of possible square matrix order 3 with each entries 0 or 1  
28. Find X and Y if  [
5 - ?? 2?? - 8
0 3
] is a scalar matrix  
29. Find X   [
4 ?? + 2
2?? - 3 ?? + 1
] is a symmetric matrix  
  
II. Two mark and Three  marks  questions (SA) 
1.Radha , fauzia, simran are the student of 12
th
 class Radha has 15 note book and 6 pens , 
Fauzia has  10 books 2 pens  and Simran has 13 books and 5 pens express this in to matrix 
forms.  
2. Construct 3× 2 matrix whose elements are given by    ?? ????
=
1
2
  |?? - 3?? | 
3. Find X,Y,Z from the equation [
?? + ?? + ?? ?? + ?? ?? + ?? ] = [
9
5
7
] 
4. Find a,b,c, d From the equation  [
?? - ?? 2?? + ?? 2?? - ?? 3?? + ?? ] = = [
-1 5
0 13
] 
5. If  A =  [
8 0
4 -2
3 6
]   B = [
2 -2
4 2
-5 1
] Find X  such that 2A + 3X = 5B 
6. Find X and Y 2[
?? 5
7 ?? - 3
] + [
3 -4
1 2
] = [
7 6
15 14
]  
7. Find X and Y  if x [
2
3
]+ ?? [
-1
1
]= [
10
5
]  
8. Given  3 [
?? ?? ?? ?? ] = [
?? 6
-1 2?? ] +  [
4 ?? + ?? ?? + ?? 3
] Fine the values  of X,Y,Z and W 
9. If ?? ?? = [
cos?? sin?? -sin?? cos?? ]  and ?? ?? =  [
cos?? sin?? -sin?? cos?? ]  Show that ?? ?? ?? ?? = ?? ?? +?? 
10. If A = [
3 -2
4 -2
] and I = [
1 0
0 1
] Find K If A
2
 = KA – 2I 
11. If A =  [
3 v3 2
4 2 0
] and B =[
2 -1 2
1 2 4
]  verify (A + B )
1
 = A
1
 +B
1
 
12. For any matrix A with real number entries , A+ A
1
 is symmetric matrix and A – A
1
 
Skew-symmetric matrix  
13. For any  matrix   A  = [
1 5
6 7
] verify that A+ A
1
 is symmetric matrix 
14. For any  matrix   A  = [
1 5
6 7
] verify that A – A
1
 Skew-symmetric matrix  
15. If A and B be the invertible matrices of same order  then (AB)
-1
 = B
-1
A
-1
 
16. By using elementary operation Find the inverse of the matrix [
1 2
2 -1
] 
17. By using elementary operation Find the inverse of the matrix [
1 3
2 7
] 
18. By using elementary operation Find the inverse of the matrix [
1 -2
2 1
] 
19. Find P
-1
 if it exists and P  = [
10 -2
-5 1
]  
20. If A = [
3 1
-1 2
] Show that A
2
 -5A +7I = 0  
21. If A = [
2 3
0 -4
] and B = [
1 5
2 0
] Show that (AB)
1
 = B
1
A
1
 
  
III. Five mark questions ( LA) 
1.If A =  [
1 1 -1
2 0 3
3 -1 2
]  B = [
1 3
0 2
-1 4
] and C =[
1 2    3   -4
2 0 -2      1
] 
Find A B , BC and show that (AB )C = A(BC)  
2. If A =  [
0 6 7
-6 0 8
7 -8 0
]  B =   [
0 1 1
1 0 2
1 2 0
]  C = [
2
-2
3
] calculate AC, BC and (A+B) C   
Deduce that (A+B) C = AC + BC  
3. If A =  [
1 2 3
3 -2 1
4 2 1
] Show that A
3
 – 23A - 40 I = 0 
4. If A =  [
1 2 -3
5 0 2
1 -1 1
]  B =  [
3 -1 2
4 2 5
2 0 3
] and C =   [
4 1 2
0 3 2
1 -2 3
]  
verify A+ (B-C) = (A+B ) –C 
5.   If A =  
[
 
 
 
 
2
3
1
5
3
1
3
2
3
4
3
7
3
2
2
3
]
 
 
 
 
   and B =   
[
 
 
 
 
2
5
3
5
1
1
5
2
5
4
5
7
5
6
5
2
5
]
 
 
 
 
   find 3A – 5B  
6. If A =  [
2 0 1
2 1 3
1 -1 0
]  find A
2
 – 5 A + 6 I ? 
Page 5


Topic: Matrices 
Question bank with solutions 
One mark question ( V S A) 
1. Define matrix  
2. Define a diagonal matrix  
3. Define scalar matrix 
4. Define symmetric matrix  
5. Define skew-symmetric matrix  
6.In a matrix       [
2 5 19  -17
35 -2
5
2
     12
v3 1 -5    17
]   
find  1) order of the matrix  
         2)  Write the elements of ?? 13
 ,?? 21
  , ?? 33
 , ?? 24
  , ?? 23
 
7. If a matrix 8 elements what is the possible order it can have ? 
8. If a matrix 18 elements  what is the possible order it can have? 
9. construct 2 × 2 matrix  [?? ????
]    whose elements are given by  
 1) ?? ????
 = (?? + ?? ) 
2
   2) ?? ????
 = 
(?? +?? ) 
2
2
  
10. construct the 2 × 3 matrix whose elements are given by   ?? ????
= |?? - ?? | 
11. Construct the 3× 2 matrix whose elements are given by   ?? ????
= 
?? ??   
12. Find x, y, z if  [
4 3
?? 5
]= [
?? ?? 1 5
]  
13. Find x, y, z if  [
?? + ?? 2
5 + ?? ????
]= [
6 2
5 8
]  
14. Find the  matrix x such that 2A + B + X =0 where A = [
-1 2
3 4
]  and B = [
3 -2
1 5
]  
15. If A = [
1 2 3
2 3 1
]     B =  [
3 -1 3
-1 0 2
]     Find 2A – B 
16. Find X if Y =[
3 2
1 4
] and 2X+Y = [
1 0
-3 2
]  
17. Find X If  X+Y = [
7 0
2 5
] and X-Y = [
3 0
0 3
]  
18. Simplify   cos?? [
cos?? sin?? -sin?? cos?? ] + sin?? [
sin?? -cos?? cos?? sin?? ]  
19. Find X If  2[
1 3
0 ?? ] + [
?? 0
1 2
] = [
5 6
1 8
] 
20. If A = [
1 2
3 4
] Find A + ?? 1
  
21. A =  [
1 -2 3
0 1 4
]     and B = [
0 2 5
6 -3 1
]     Find 3A + 2B  
22. if  A = [
sin?? cos?? -cos?? sin?? ] Verify A A
1
 = I  
23. if B = [
cos?? sin?? -sin?? cos?? ] verify B B
1
= I 
24. If A = [
0
1
2
]  B = [
1 5 7
] Find AB 
25. Compute  1) [
1 -2
2 3
] [
1 2 3
2 3 1
]  
           2) [
3 -1 3
-1 0 2
][
2 -3
1 0
3 1
] 
26. Find X and Y [
2?? + ?? 3?? 6 4
]  =  [
6 0
6 4
] 
27. What is the number of possible square matrix order 3 with each entries 0 or 1  
28. Find X and Y if  [
5 - ?? 2?? - 8
0 3
] is a scalar matrix  
29. Find X   [
4 ?? + 2
2?? - 3 ?? + 1
] is a symmetric matrix  
  
II. Two mark and Three  marks  questions (SA) 
1.Radha , fauzia, simran are the student of 12
th
 class Radha has 15 note book and 6 pens , 
Fauzia has  10 books 2 pens  and Simran has 13 books and 5 pens express this in to matrix 
forms.  
2. Construct 3× 2 matrix whose elements are given by    ?? ????
=
1
2
  |?? - 3?? | 
3. Find X,Y,Z from the equation [
?? + ?? + ?? ?? + ?? ?? + ?? ] = [
9
5
7
] 
4. Find a,b,c, d From the equation  [
?? - ?? 2?? + ?? 2?? - ?? 3?? + ?? ] = = [
-1 5
0 13
] 
5. If  A =  [
8 0
4 -2
3 6
]   B = [
2 -2
4 2
-5 1
] Find X  such that 2A + 3X = 5B 
6. Find X and Y 2[
?? 5
7 ?? - 3
] + [
3 -4
1 2
] = [
7 6
15 14
]  
7. Find X and Y  if x [
2
3
]+ ?? [
-1
1
]= [
10
5
]  
8. Given  3 [
?? ?? ?? ?? ] = [
?? 6
-1 2?? ] +  [
4 ?? + ?? ?? + ?? 3
] Fine the values  of X,Y,Z and W 
9. If ?? ?? = [
cos?? sin?? -sin?? cos?? ]  and ?? ?? =  [
cos?? sin?? -sin?? cos?? ]  Show that ?? ?? ?? ?? = ?? ?? +?? 
10. If A = [
3 -2
4 -2
] and I = [
1 0
0 1
] Find K If A
2
 = KA – 2I 
11. If A =  [
3 v3 2
4 2 0
] and B =[
2 -1 2
1 2 4
]  verify (A + B )
1
 = A
1
 +B
1
 
12. For any matrix A with real number entries , A+ A
1
 is symmetric matrix and A – A
1
 
Skew-symmetric matrix  
13. For any  matrix   A  = [
1 5
6 7
] verify that A+ A
1
 is symmetric matrix 
14. For any  matrix   A  = [
1 5
6 7
] verify that A – A
1
 Skew-symmetric matrix  
15. If A and B be the invertible matrices of same order  then (AB)
-1
 = B
-1
A
-1
 
16. By using elementary operation Find the inverse of the matrix [
1 2
2 -1
] 
17. By using elementary operation Find the inverse of the matrix [
1 3
2 7
] 
18. By using elementary operation Find the inverse of the matrix [
1 -2
2 1
] 
19. Find P
-1
 if it exists and P  = [
10 -2
-5 1
]  
20. If A = [
3 1
-1 2
] Show that A
2
 -5A +7I = 0  
21. If A = [
2 3
0 -4
] and B = [
1 5
2 0
] Show that (AB)
1
 = B
1
A
1
 
  
III. Five mark questions ( LA) 
1.If A =  [
1 1 -1
2 0 3
3 -1 2
]  B = [
1 3
0 2
-1 4
] and C =[
1 2    3   -4
2 0 -2      1
] 
Find A B , BC and show that (AB )C = A(BC)  
2. If A =  [
0 6 7
-6 0 8
7 -8 0
]  B =   [
0 1 1
1 0 2
1 2 0
]  C = [
2
-2
3
] calculate AC, BC and (A+B) C   
Deduce that (A+B) C = AC + BC  
3. If A =  [
1 2 3
3 -2 1
4 2 1
] Show that A
3
 – 23A - 40 I = 0 
4. If A =  [
1 2 -3
5 0 2
1 -1 1
]  B =  [
3 -1 2
4 2 5
2 0 3
] and C =   [
4 1 2
0 3 2
1 -2 3
]  
verify A+ (B-C) = (A+B ) –C 
5.   If A =  
[
 
 
 
 
2
3
1
5
3
1
3
2
3
4
3
7
3
2
2
3
]
 
 
 
 
   and B =   
[
 
 
 
 
2
5
3
5
1
1
5
2
5
4
5
7
5
6
5
2
5
]
 
 
 
 
   find 3A – 5B  
6. If A =  [
2 0 1
2 1 3
1 -1 0
]  find A
2
 – 5 A + 6 I ? 
7. If A =  [
1 0 2
0 2 1
2 0 3
]  prove that A
3
 – 6A
2
 + 7A + 2I = 0 
8. Express the matrix B =  [
2 -2 -4
-1 3 4
1 -2 -3
]  Find the sum of symmetric and skew-
symmetric matrix  
9. Express the matrix B =  [
6 -2 2
-2 3 -1
2 -1 3
]  Find the sum of symmetric and skew-
symmetric matrix  
10. If A = [
1 2
2 1
] B = [
2 0
1 3
] C = [
1 1
2 3
] calculate AB , BC, A(B+C)  
Verify that AB + AC = A(B+C)  
11. If F(x) = [
cos?? -sin?? 0
sin?? cos?? 0
0 0 1
] show that F(x) F(y) = F(x+y)  
12. If A =[
-2
4
5
] and B = [
1 3 -6
]  verify (AB)
1
 = B
1
A
1
 
13. If A = [
cos?? sin?? -sin?? cos?? ] Prove that A
n
 =  [
cos???? sin????
-sin???? cos????
]  
 
 
 
********

FAQs on Matrices - Question Bank, Mathematics, Engineering, Semester - Engineering Mathematics

1. What are matrices in Mathematics?

Ans. In Mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is used to represent and manipulate systems of linear equations, transformations in geometry, and other mathematical operations.

2. What are the types of matrices?

Ans. There are several types of matrices in Mathematics, including square matrices, rectangular matrices, diagonal matrices, upper triangular matrices, lower triangular matrices, identity matrices, null matrices, symmetric matrices, skew-symmetric matrices, and orthogonal matrices.

3. What is the determinant of a matrix?

Ans. The determinant of a matrix is a scalar value that can be calculated from the elements of the matrix. It is used to determine properties of the matrix, such as whether it is invertible, and to solve systems of linear equations. The determinant is calculated by summing the products of the elements of each row or column, multiplied by their corresponding cofactors.

4. How are matrices used in Engineering?

Ans. Matrices are used extensively in Engineering to represent and manipulate data, such as structural loads, electrical circuits, and thermal systems. They are used to solve complex systems of equations, optimize designs, and simulate real-world scenarios in fields like mechanical, civil, electrical, and chemical engineering.

5. What is the transpose of a matrix?

Ans. The transpose of a matrix is obtained by interchanging its rows and columns. It results in a new matrix with the same dimensions as the original matrix, but with the rows and columns switched. The transpose is useful in many applications, such as solving systems of linear equations, calculating eigenvalues and eigenvectors, and performing matrix multiplication.

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