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Matrices and Determinants

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  1. 1.If the system of linear equations : gathered x+y+z=6 x+2y+5z=10 2x+3y+ z= gathered has inf…
  2. 2.Let A=[[|gathered 1 2 2 3 0 0 4 5 gathered]]| and B=[[|gathered 1 0 0 0 -5 0 0 4 -2 gather…
  3. 3.The sum of all possible values of [0,2 ], for which the system of equations : gathered x 3…
  4. 4.Let A=[[|gathered 1 0 0 3 1 0 9 3 1 gathered]]| and B=[b_ij],1 i,j 3.
  5. 5.If f:N Z is defined by f(n)=vmatrix n -1 -5 -2n^2 3(2k+1) 2k+1 -3n^3 3k(2k+1) 3k(k+2)+1 vm…
  6. 6.Let M be a 3 3 matrix such that M((|gathered 1 0 0 gathered))|=((|gathered 1 2 3 gathered)…
  7. 7.Let A be a 3 3 matrix such that A^T[[|gathered 1 0 1 gathered]]|=[[|gathered 5 2 2 gathere…
  8. 8.Consider the system of linear equations in x,y,z : gathered x+2y+tz=0 6x+y+5tz=0 3x+t^2y+f…
  9. 9.If the system of equations : gathered x+y+z=5 x+2y+3z=9 x+3y+ z= gathered has infinitely m…
  10. 10.Let A=[[|gathered 1 2 7 4 -2 8 3 8 -7 gathered]]| and (A- I)=0, where is a real number.
  11. 11.Let S=A=[array|c|c| a & b c & d array]:a,b,c,d 0,1,2,3,4 and A^2-4A+3I=0 be a set of 2 2 m…
  12. 12.Let A=[[|gathered 1 1 2 -2 0 1 1 3 5 gathered]]|.
  13. 13.If the system of equations x + 5y + 6z = 4 2x + 3y + 4z = 7 x + 6y + az = b has infinitely…
  14. 14.Let , R be such that the system of linear equations array|c|c| x+2y+z & =5 2x+y+ z & =5 8x…
  15. 15.Let A=[array|c|c| 1 & 2 1 & array] and B=[array|c|c| 3 & 3 & 2 array].
  16. 16.Let A, B and C be three 2 2 matrices with real entries such that B=(I+A)^-1 and A+C=I.
  17. 17.Let P=[p_ij] and Q=[q_ij] be two square matrices of order 3 such that q_ij=2^(i+j-1)p_ij a…
  18. 18.Let f(x)= 7x^10+9x^8(1+x^2+2x^9)^2dx,x>0,x 0limf(x)=0 and f(1)=(1)/(4).
  19. 19.The system of linear equations gathered x+y+z=6 2x+5y+az=36 x+2y+3z=b gathered has :
  20. 20.Among the statements : I: If vmatrix 1 1 1 vmatrix=vmatrix 0 0 0 vmatrix, then ^2 + ^2 + ^…
  21. 21.Let n be the number obtained on rolling a fair die.
  22. 22.If X=[[|gathered x y z gathered]]| is a solution of the system of equations AX=B, where ad…
  23. 23.If A=[array|c|c| 2 & 3 3 & 5 array], then the determinant of the matrix (A^2025-3A^2024+A^…
  24. 24.If the system of equations 3x+y+4z=3 2x+ y-z=-3 x+2y+z=4 has no solution, then the value o…
  25. 25.For the matrices A=[array|c|c| 3 & -4 1 & -1 array] and B=[array|c|c| -29 & 49 -13 & 18 ar…
  26. 26.Let be a solution of x^2+x+1=0, and for some a and b in R,[gathered 4 a b gathered][[|gath…
  27. 27.Let A=[[|gathered 2 2+p 2+p+q 4 6+2p 8+3p+2q 6 12+3p 20+6p+3q gathered]]|.
  28. 28.Let the system of equations x + 5y - z = 1 4x + 3y - 3z = 7 24x + y + z = , R, have infini…
  29. 29.Let A be a 3 3 matrix such that |adj(adj(adjA))|=81.
  30. 30.Let the system of equations : gathered 2x+3y+5z=9 7x+3y-2z=8 12x+3y-(4+ )z=16- gathered ha…
  31. 31.Let the matrix A=[[|gathered 1 0 0 1 0 1 0 1 0 gathered]]| satisfy A^n=A^n-2+A^2-I for n 3…
  32. 32.Let A be a matrix of order 3 3 and |A|=5.
  33. 33.If the system of equations gathered 2x+ y+3z=5 3x+2y-z=7 4x+5y+ z=9 gathered has infinitel…
  34. 34.Let A be a 3 3 real matrix such that A^2(A-2 I)-4(A-I)=O, where I and O are the identity a…
  35. 35.Let A=[array|c|c| & -1 6 & array], >0, such that (A)=0 and + =1.
  36. 36.Let a R and A be a matrix of order 3 3 such that (A)=-4 and A+I=[[|gathered 1 a 1 2 1 0 a …
  37. 37.If the system of linear equations [ aligned & 3 x+y+ z=3 & 2 x+ y-z=-3 & x+2 y+z=4 aligned…
  38. 38.Let A = [a_ij] be a 2 2 matrix such that a_ij 0, 1 for all i and j.
  39. 39.Let , ( ) be the values of m, for which the equations x+y+z=1, x+2y+4z=m and x+4y+10z=m^2 …
  40. 40.Let A=[a_ij] be a matrix of order 3 3, with a_ij=(√2)^i+j.
  41. 41.Let A=[gathered a_ij gathered]=[array|c|c| _5128 & _45 _58 & _425 array].
  42. 42.Let M and m respectively be the maximum and the minimum values of f(x)=vmatrix 1+ ^2x ^2x …
  43. 43.Let A=[array|c|c| 1√2 & -2 0 & 1 array] and P=[array|c|c| & - & array], >0.
  44. 44.For some a,b, let f(x)=vmatrix a+( x)/(x) 1 b a 1+( x)/(x) b a 1 b+( x)/(x) vmatrix,x 0,x …
  45. 45.If the system of equations gathered 2x-y+z=4 5x+ y+3z=12 100x-47y+ z=212 gathered has infi…
  46. 46.The system of equations gathered x+y+z=6, x+2y+5z=9, x+5y+ z= , gathered has no solution i…
  47. 47.Let A=[a_ij] be a 3 3 matrix such that A[[|gathered 0 1 0 gathered]]|=[[|gathered 0 0 1 ga…
  48. 48.If the system of equations gathered ( -1)x+( -4)y+ z=5 x+( -1)y+( -4)z=7 ( +1)x+( +2)y-( +…
  49. 49.If A,B,and(adj(A^-1)+adj(B^-1)) are non-singular matrices of same order, then the inverse …
  50. 50.If the system of linear equations : gathered x+y+2z=6 2x+3y+az=a+1 -x-3y+bz=2b gathered wh…