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Matrices and Determinants

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  1. 51.For a 3 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M.
  2. 52.Let B=[array|c|c| 1 & 3 1 & 5 array] and A be a 2 2 matrix such that AB^-1=A^-1.
  3. 53.Let , R.
  4. 54.If a, b, c and vmatrix b c a c a b vmatrix=0, then (a)/( -a)+(b)/( -b)+( )/( -c) is equal …
  5. 55.If the system of equations x+4y-z= ,7x+9y+ z=-3,5x+y+2z=-1 has infinitely many solutions, …
  6. 56.Let A=[[|gathered 2 a 0 1 3 1 0 5 b gathered]]|.
  7. 57.If A is a square matrix of order 3 such that (A)=3 and (adj(-4adj(-3adj(3adj((2A)^-1)))))=…
  8. 58.For , R and a natural number n, let A_r=vmatrix r 1 n^22+ 2r 2 n^2- 3r-2 3 (n(3n-1))/(2) v…
  9. 59.The values of m,n, for which the system of equations gathered x+y+z=4, 2x+5y+5z=17, x+2y+m…
  10. 60.Let 0 and A=[[|gathered 3 - 2 gathered]]|.
  11. 61.Let A and B be two square matrices of order 3 such that |A|=3 and |B|=2.
  12. 62.If the system of equations gathered 11x+y+ z=-5 2x+3y+5z=3 8x-19y-39z= gathered has infini…
  13. 63.Let A=[array|c|c| 1 & 2 0 & 1 array] and B=I+adj(A)+(adjA)^2+ +(adjA)^10.
  14. 64.Let (0,) and A=[[|gathered 1 2 1 0 1 0 1 2 gathered]]|.
  15. 65.If the system of equations gathered x+(√2 )y+(√2 )z=0 x+( )y+( )z=0 x+( )y-( )z=0 gathered…
  16. 66.Let the system of equations x+2y+3z=5,2x+3y+z=9,4x+3y+ z= have infinite number of solution…
  17. 67.If A=[array|c|c| √2 & 1 -1 & √2 array],B=[array|c|c| 1 & 0 1 & 1 array],C=ABA^T and X=A^TC…
  18. 68.If the system of equations gathered 2x+3y-z=5 x+ y+3z=-4 3x-y+ z=7 gathered has infinitely…
  19. 69.Let A be a 3 3 real matrix such that A((|gathered 1 0 1 gathered))|=2((|gathered 1 0 1 gat…
  20. 70.If the system of linear equations gathered x-2y+z=-4 2x+ y+3z=5 3x-y+ z=3 gathered has inf…
  21. 71.Let R=((|gathered x 0 0 0 y 0 0 0 z gathered))| be a non-zero 3 3 matrix, where x =y ( +(2…
  22. 72.Consider the system of linear equations x+y+z=5,x+2y+ ^2z=9,x+3y+ z= , where , R.
  23. 73.Consider the system of linear equations x+y+z=4 ,x+2y+2 z=10 ,x+3y+4 ^2z= ^2+15 where , R.
  24. 74.Let A=[[|gathered 2 1 2 6 2 11 3 3 2 gathered]]| and P=[[|gathered 1 2 0 5 0 2 7 1 5 gathe…
  25. 75.A=[[|gathered 1 0 0 0 0 gathered]]||2A|^3=2^21 , Z
  26. 76.Let A be a square matrix such that AA^T=I.
  27. 77.The values of , for which vmatrix 1 (3)/(2) +(3)/(2) 1 (1)/(3) +(1)/(3) 2 +3 3 +1 0 vmatri…
  28. 78.Consider the matrix f(x)=[[|gathered x - x 0 x x 0 0 0 1 gathered]]|.
  29. 79.Let the determinant of a square matrix A of order m be m-n, where m and n satisfy 4 m+n=22…
  30. 80.Let for A=[[|gathered 1 2 3 3 1 1 1 2 gathered]]|,|A|=2.
  31. 81.If the system of equations 2x+y-z=5 2x-5y+ z= x+2y-5z=7 has infinitely many solutions, the…
  32. 82.For the system of linear equations 2 x+4 y+2 a z=b x+2 y+3 z=4 2 x-5 y+2 z=8 which of the …
  33. 83.Let B=[[|gathered 1 3 1 2 3 4 gathered]]|, >2 be the adjoint of a matrix A and |A|=2.
  34. 84.The number of symmetric matrices of order 3, with all the entries from the set [0,1,2,3,4,…
  35. 85.Let A=[array|c|c| 1 & (1)/(51) 0 & 1 array].
  36. 86.If the system of linear equations gathered 7x+11y+ z=13 5x+4y+7z= 175x+194y+57z=361 gather…
  37. 87.vmatrix x+1 x x x x+ x x x x+ ^2 vmatrix=(9)/(8)(103x+81), then ,( )/(3) are the roots of …
  38. 88.Let A be a 2 2 matrix with real entries such that A^'= A+I, where R--1,1.
  39. 89.If A=(1)/(5!6!7!)[[|gathered 5!
  40. 90.If A is a 3 [] 3 matrix and |A| = 2, then [|3,adj,(|3A|A^2)|] is equal to :
  41. 91.For the system of linear equations 2x-y+3z=5 3x+2y-z=7 4x+5y+ z= , which of the following …
  42. 92.If A=[array|c|c| 1 & 5 & 10 array],A^-1= A+ I and + =-2, then 4 ^2+ ^2+ ^2 is equal to :
  43. 93.Let S be the set of all values of [- , ] for which the system of linear equations x+y+√3z=…
  44. 94.Let A=[[|gathered 2 1 0 1 2 -1 0 -1 2 gathered]]|.
  45. 95.Let P=[[|array|c|c| √32 & (1)/(2) -(1)/(2) & √32 array]]|,A=[array|c|c| 1 & 1 0 & 1 array]…
  46. 96.Let P be a square matrix such that P^2=I-P.
  47. 97.For the system of equations x+y+z=6 x+2y+ z=10 x+3y+5z= , which one of the following is NO…
  48. 98.If the system of equations x+y+a z=b 2 x+5 y+2 z=6 x+2 y+3 z=3 has infinitely many solutio…
  49. 99.Let A=[a_ij]_2 2, where a_ij 0 for all i,j and A^2=I.
  50. 100.For , R, suppose the system of linear equations gathered x-y+z=5 2x+2y+ z=8 3x-y+4z= gathe…