CLASS 12 MATRICES DPP
CLASS – XII
1. If A= [(3&-2@4&2)] find K in A² = KA+2I.
2. Find x & y in [■(x+3&4@y-4&x+y)] = [■(5&4@3&9)]
3. If A = [1 2 3] find AA'.
4. Find the number of possible matrices of 2x2 with each entry 1 or 2.
5. Write a square matrix which is both symmetry and skew symmetry.
6. If A(adj A) = [■(-2&0&0@0&-2&0@0&0&-2)]. Find |A|
7. If B = [■(1&-5@0&-3)] and A+2B = [■(0&4@-7&5)] Find A.
8. If A= [1 4 4] and B=[■(2@5@6)] find AB.
9. Simplify sin θ [■(sinθ&-cosθ@cosθ&sinθ)] + cos θ [■(cosθ&sinθ@-sinθ&cosθ)] – diag(-1,1) ?
10. If A=[■(2&3@1&2)]. Prove that A³-4A2+A=0
11. Find x If [1 x 1] [■(1&2&3@4&5&6@3&2&3)][■(1@-2@3)]=[]
12. Express as sum of symm and skew symm
i) [■(1&3&5@-6&8&3@4&6&5)] (ii) [■(6&2@8&9)]
13. If [■(cos〖2π/5〗&-sin2π/5@sin〖2π/5〗&cos2π/5)]k = [■(1&0@0&1)]. Find least positive value of K.
14. A = [■(1&3&4@-2&5&7)] and 2A-3B = [■(4&5&-4@1&2&3)]. Find B.
15. find x+y from the following
2[■(x&5@7&y-3)]+ [■(3&-4@1&2)]= [■(7&6@15&14)]
16. Simplify
tan θ [■(secθ&tan θ@tan θ&-sec θ)] + sec θ[■(-tanθ&-sec θ@-sec θ&tan θ)]
17. If A = [■(2&4@3&2)] and B= [■(-2&5@3&4)] find 3A – B ?
18. If A = [0 0 1] then A⁶ is equal to _____
[0 1 0]
[1 0 0]
19. If A, B are symmetric matrix. Prove that AB+BA is symm. and AB-BA is
skew Symm.
20. Prove that sum of diagonal elements & skew symm. always zero.
21. Verify that (AB)'=B'A'. For A=[■(1@-4@3)], B= [-1 2 1]
22. If A =[■(2&-3&5@3&2&-4@1&1&-4)] find A⁻¹. Using A⁻¹ solve the following equation
2x - 3y + 5z = 16, 3x + 2y - 4z = -4, x + y - 2z = -3
23. Solve the system of following
2/x + 3/y + 10/z = 4, 4/x - 6/y + 5/z = 1
6/x + 9/y - 20/z = 2
24. A =[■(1&-1&2@2&3&-3@0&1&4)][■(-2&0&1@9&2&-3@6&1&-2)] . Verify that BA = 6I, use the result to
solve the equation x - y = 3 2x + 3y + 4z = 17
y + 2z = 7
25. Use the product
[■(1&-1&2@0&2&-3@3&-2&4)][■(-2&0&1@9&2&-3@6&1&-2)] to solve the equation x + 3z = 90,
-x + 2y - 2z = 4 2x - 3y + 4z = -3
26. Determine the Product
[■(-4&4&4@-7&1&3@5&-3&-1)][■(1&-1&1@1&-2&-6@2&1&3)] and solve the equation
x - y + z = 4
x - 2y - 2z = 9
2x + y + 3z = 1
27. If A = [■(3&2@7&5)] B = [■(4&6@3&2)]. Verify that (AB)⁻¹ = B⁻¹A⁻¹
28. If A = [■(2&-3&5@3&2&-4@1&1&-2)] find A⁻¹, use it to solve the system of equation.
2x - 3y + 5z = 11
3x + 2y - 4z = -5
x + y - 2z = -3
29. A is invertible matrix of 3x3 and |A|=9, find |A⁻¹|
30. For what k, [■(k&2@3&4)] has no inverse.
31. Given a square matrin 3x3 such that |A|=12. find |adj(adj(A))|
32. If A is a square matrin of 3x3 such that A (adj(A)) = 10I then find
|adjA.A|
33. If A is skew symmetric matrix of 3x3 then find |A|.
34. If A = [■(3&0&0@0&3&0@0&0&3)] find |A.adj(A)|
35. If A and B are invertible matrix of same order. Given |(AB)⁻¹|=8, |A|=¾
find |B|
36. If A [■(k&10@7&k-3)]= is a Singular. matrin find k.
37. Find A⁻¹ of A =[■(2&5@1&3)]
38. If A is 3x3 matrin then what will be the value of k if det(A⁻¹) = (detA)k
39. If |A|=3 and A⁻¹[■(3&-1@-5/3&1/3)]= find adj(A).
40. If A = [■(2&3@5&-2)]be such that A⁻¹ = KA find k.
41. If A [■(1&2@3&4)] = [■(1&-1@0&0@2&3)]find A⁻¹
42. If A⁻¹ = [■(3&-1&1@-15&6&-5@5&-2&2)] B=[■(1&2&-2@-1&3&0@0&-2&1)] find (AB⁻¹).
43. If A and B are invertible matrin such that |(AB)⁻¹| = 8 and |A| = 2 then
find |B|
44. If A =[■(2x&0@x&x)], A-1 = [■(1&0@-1&2)]. Find x
* * * * * * * * * * * * *
