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Matrices and Determinants

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  1. 401.Let the system of linear equations x + y + []z = 2 3x + y + z = 4 x + 2z = 1 have a unique…
  2. 402.The number of values of [] for which the system of equations : x + y + z = [] []x + 2[]y +…
  3. 403.Let S = [n] : 1 [] n [] 50 and n is odd.
  4. 404.The number of [ (0,4 )] for which the system of linear equations [ aligned &3( 3 ) x-y+z=2…
  5. 405.Let A be a 3 [] 3 real matrix such that [A( pmatrix 1 1 0 pmatrix ) = ( pmatrix 1 1 0 pmat…
  6. 406.Let [A = [ pmatrix 0 & - 2 2 & 0 pmatrix ]].
  7. 407.If the system of linear equations.
  8. 408.The ordered pair (a, b), for which the system of linear equations 3x - 2y + z = b 5x - 8y …
  9. 409.Let [A=([gathered 4 -2 gathered])].
  10. 410.Let [A=([arraycc 1 & 2 -2 & -5 array])].
  11. 411.Let A and B be two 3 [] 3 matrices such that AB = I and [|A| = 1 8].
  12. 412.Let the system of linear equations x + 2y + z = 2, [ x + 3y - z = ], [ - x + y + 2z = - ] …
  13. 413.Let the matrix [A=[[arraylll 0 & 1 & 0 0 & 0 & 1 1 & 0 & 0 array]]] and the matrix B_0=A^4…
  14. 414.If the system of linear equations 2x + 3y - z = - 2 x + y + z = 4 [x - y + | |z = 4 - 4] w…
  15. 415.Let A be a matrix of order 3 [] 3 and det (A) = 2.
  16. 416.Which of the following matrices can NOT be obtained from the matrix [[[arraycc -1 & 2 1 & …
  17. 417.If the system of equations [ aligned &x+y+z=6 &2 x+5 y+ z= &x+2 y+3 z=14 aligned ] has inf…
  18. 418.If the system of linear equations 2x + y - z = 7 x - 3y + 2z = 1 x + 4y + []z = k, where […
  19. 419.Let A and B be two square matrices of order 2.
  20. 420.If [A=15 !
  21. 421.If the system of linear equations [ aligned & 7 x+11 y+ z=13 & 5 x+4 y+7 z= & 175 x+194 y+…
  22. 422.[|[arrayccc x+1 & x & x x & x+ & x x & x & x+^2 array]|=(9)/(8)(103 x+81)], then [, ()/(3)…
  23. 423.Let [A] be a [2 2] matrix with real entries such that [A'= A+I], where [ R--1,1].
  24. 424.Let for [A = [ pmatrix 1 & 2 & 3 & 3 & 1 1 & 1 & 2 pmatrix ],|A| = 2].
  25. 425.If the system of equations 2 x+y-z=5 [2 x-5 y+ z=] x+2 y-5 z=7 has infinitely many solutio…
  26. 426.For the system of linear equations [ x+y+z=1,x+ y+z=1,x+y+ z=], which one of the following…
  27. 427.Let S denote the set of all real values of [] such that the system of equations [ x+y+z=1]…
  28. 428.If the system of equations x+2y+3z=3 4x+3y-4z=4 [8x+4y- z=9+] has infinitely many solution…
  29. 429.Let S_1 and S_2 be respectively the sets of all [a R - 0 ] for which the system of linear …
  30. 430.Let [] and [] be real numbers.
  31. 431.Consider the following system of equations [ x+2y+z=1] [2 x+3y+z=1] [3x+ y+2z=] for some […
  32. 432.For , R, suppose the system of linear equations [ aligned & x-y+z=5 & 2 x+2 y+ z=8 & 3 x-y…
  33. 433.Let the system of linear equations x+y+kz=2 2x+3y-z=1 3x+4y+2z=k have infinitely many solu…
  34. 434.Let [A=([arraycc m & n p & q array]), d=|A| 0] and [|A-d(A d j A)|=0].
  35. 435.For the system of linear equations x+y+z=6 [ x+ y+7 z=3] x+2 y+3 z=14 which of the followi…
  36. 436.Let [A = ( pmatrix 1 & 0 & 0 0 & 4 & - 1 0 & 12 & - 3 pmatrix )].
  37. 437.Let P be a square matrix such that P^2=I-P.
  38. 438.Let [A=[[arrayccc 2 & 1 & 0 1 & 2 & -1 0 & -1 & 2 array]]].
  39. 439.Let [P=[[arraycc √32 & (1)/(2) -(1)/(2) & √32 array]], A=[[arrayll 1 & 1 0 & 1 array]]] an…
  40. 440.The values of [], for which [|[arrayccc 1 & (3)/(2) & +(3)/(2) 1 & (1)/(3) & +(1)/(3) 2 +3…
  41. 441.Consider the matrix f(x)=[arrayccc x & - x & 0 x & x & 0 0 & 0 & 1 array].
  42. 442.Let [A=[[arrayccc 2 & 1 & 2 6 & 2 & 11 3 & 3 & 2 array]]] and [P=[[arraylll 1 & 2 & 0 5 & …
  43. 443.[ Let A=[[arraylll 1 & 0 & 0 0 & & 0 & & array]] and |2 ~A|^3=2^21 where , Z , Then a valu…
  44. 444.Consider the system of linear equations [x+y+z=5, x+2 y+^2 z=9, x+3 y+ z=], where [, R].
  45. 445.Consider the system of linear equations [x+y+z=4 , x+2 y+2 z=10 , x+3 y+4 ^2 z=^2+15] wher…
  46. 446.Let A be a [3 3] real matrix such that [A([gathered 1 0 1 gathered])=2([gathered 1 0 1 gat…
  47. 447.If the system of linear equations [aligned & x-2 y+z=-4 & 2 x+ y+3 z=5 & 3 x-y+ z=3 aligne…
  48. 448.Let [A=[[arrayll 1 & 2 0 & 1 array]]] and [B=I+adj(A)+(adj A)^2++(adj A)^10].
  49. 449.Let [ (0, )] and [A=[[arraylll 1 & 2 & 1 & 0 & 1 0 & 1 & 2 array]]].
  50. 450.If the system of equations [aligned & x+(√2 ) y+(√2 ) z=0 & x+( ) y+( ) z=0 & x+( ) y-( ) …