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Matrices and Determinants

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  1. 101.If the system of equations []x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = [] has infinite…
  2. 102.The system of equations - kx + 3y - 14z = 25 - 15x + 4y - kz = 3 - 4x + y + 3z = 4 is cons…
  3. 103.The system of linear equations 3x - 2y - kz = 10 2x - 4y - 2z = 6 x+2y - z = 5m is inconsi…
  4. 104.The following system of linear equations 7x + 6y -- 2z = 0 3x + 4y + 2z = 0 x -- 2y -- 6z …
  5. 105.If the system of equations x + y + z = 5 x + 2y + 3z = 9 x + 3y + az = [ ] has infinitely …
  6. 106.Let A=[[|gathered -1 1 -1 1 0 1 0 0 1 gathered]]| satisfy A^2+ (adj(adj(A)))+ (adj(A)(adj(…
  7. 107.Consider the matrices A=[array|c|c| 2 & -2 4 & -2 array] and B=[array|c|c| 3 & 9 1 & 3 arr…
  8. 108.Let A=[array|c|c| 3 & -4 1 & -1 array] and B be two matrices such that A^100=100B+I.
  9. 109.The number of 3 2 matrices A , which can be formed using the elements of the set -2,-1,0,1…
  10. 110.Let A=[[|gathered 0 2 -3 -2 0 1 3 -1 0 gathered]]| and B be a matrix such that B(I-A)=I+A.
  11. 111.Let |A|=6, where A is a 3 3 matrix.
  12. 112.Let A be a 3 3 matrix such that A+A^T=O.
  13. 113.For some , R, let A=[array|c|c| & 2 1 & 2 array] and B=[array|c|c| 1 & 1 1 & array] be suc…
  14. 114.The number of singular matrices of order 2 , whose elements are from the set 2,3,6,9, is _…
  15. 115.Let A=[[|gathered 0 - 0 1 0 0 gathered]]|.
  16. 116.Let I be the identity matrix of order 3 3 and for the matrix A=[[|gathered 2 3 4 5 6 7 -1 …
  17. 117.Let S=m Z:A^m^2+A^m=3I-A^-6, where A=[array|c|c| 2 & -1 1 & 0 array].
  18. 118.Let M denote the set of all real matrices of order 3 3 and let S=-3,-2,-1,1,2.
  19. 119.Let A be a 3 3 matrix such that X^TAX=O for all nonzero 3 1 matrices X=[[|gathered x y z g…
  20. 120.Let A be a square matrix of order 3 such that (A)=-2 and (3adj(-6adj(3A)))=2^m+n 3^mn,m>n.
  21. 121.Consider the matrices : A=[array|c|c| 2 & -5 3 & m array],B=[gathered 20 m gathered] and X…
  22. 122.Let A be a non-singular matrix of order 3.
  23. 123.Let A=[array|c|c| 2 & -1 1 & 1 array].
  24. 124.If the system of equations gathered 2x+7y+ z=3 3x+2y+5z=4 x+ y+32z=-1 gathered has infinit…
  25. 125.Let =45; , , R.
  26. 126.Let A be a 2 2 symmetric matrix such that A[gathered 1 1 gathered]=[gathered 3 7 gathered]…
  27. 127.Let A be a square matrix of order 2 such that |A|=2 and the sum of its diagonal elements i…
  28. 128.Let A be a 3 3 matrix of non-negative real elements such that A[[|gathered 1 1 1 gathered]…
  29. 129.Let A=I_2-2 M M^T, where M is a real matrix of order 2 1 such that the relation M^T M=I_1 …
  30. 130.Let A be a 3 3 matrix and (A)=2.
  31. 131.Let for any three distinct consecutive terms a, b, c of an A.P, the lines a x+b y+c=0 be c…
  32. 132.Let A be a [2 2] real matrix and I be the identity matrix of order 2.
  33. 133.Let A=[[|gathered 2 0 1 1 1 0 1 0 1 gathered]]|,B=[B_1,B_2,B_3], where B_1,B_2,B_3 are col…
  34. 134.Let D_k=vmatrix 1 2k 2k-1 n n^2+n+2 n^2 n n^2+n n^2+n+2 vmatrix.
  35. 135.Let A=[[|gathered 0 1 2 a 0 3 1 c 0 gathered]]|, where a,c R.
  36. 136.Let S be the set of values of , for which the system of equations 6 x-3y+3z=4 ^2, 2x+6 y+4…
  37. 137.Let A be a n n matrix such that |A|=2.
  38. 138.If A=12bmatrix1 & √3-√3 & 1bmatrix, then:
  39. 139.For some ,R, let A=pmatrix & 2 1 & 2pmatrix and B=pmatrix1 & 1 1 & pmatrix be such that A^…
  40. 140.Let A be a 3 3 matrix such that A+A^T=O (i.e.
  41. 141.Let A be a 3 3 matrix with |A|=6.
  42. 142.Let A=pmatrix0&2&-3-2&0&13&-1&0pmatrix and B be a matrix such that B(I-A)=I+A.
  43. 143.The number of 3 2 matrices A=pmatrixa&b&d&fpmatrix with a,b,c,d,e,f-2,-1,0,1,2, for which …
  44. 144.Let A=pmatrix3&-41&-1pmatrix and B be such that A^100=100B+I.
  45. 145.Consider the matrices A=pmatrix2&-24&-2pmatrix and B=pmatrix3&91&3pmatrix.
  46. 146.Let A=pmatrix-1&1&-11&0&10&0&1pmatrix.
  47. 147.For the matrices A=pmatrix3&-41&-1pmatrix and B=pmatrix-29&49-13&18pmatrix, if (A^15+B)pma…
  48. 148.If A=pmatrix2&33&5pmatrix with |A|=1, then the determinant of the matrix A^2025-3A^2024+A^…
  49. 149.If X=pmatrixxpmatrix is a solution of the system of equations AX=B, where adj(A)=pmatrix4&…
  50. 150.Let n be the number obtained on rolling a fair die.