questionrEarly access

Matrices and Determinants

Showing 50 of 472 · 472 total
  1. 351.Let A = [( pmatrix 0 & 2q & r p & q & - r p & - q & r pmatrix ).] If AAT = I3, then [| p |…
  2. 352.If A is a symmetric matrix and B is a skew-symmetric matrix such that A + B = [[ pmatrix 2…
  3. 353.If [B = [ pmatrix 5 & 2 & 1 0 & 2 & 1 & 3 & - 1 pmatrix ]] is the inverse of a 3 3 matrix …
  4. 354.If A = [[ pmatrix 1 & & 1 - & 1 & - 1 & - & 1 pmatrix ]]; then for all [ ] [ ] [( 3 4,5 4 …
  5. 355.The set of all values of [ ] for which the system of linear equations x -- 2y -- 2z = [ ]x…
  6. 356.An ordered pair ([ ], [ ]) for which the system of linear equations (1 + [ ]) x + [ ]y + z…
  7. 357.Let [A = ( pmatrix & - & pmatrix )], ([ ] [ ] R) such that [A^32 = ( pmatrix 0 & - 1 1 & 0…
  8. 358.The greatest value of c [ ] R for which the system of linear equations x -- cy -- cz = 0 c…
  9. 359.If the system of equations 2x + 3y -- z = 0, x + ky -- 2z = 0 and 2x -- y + z = 0 has a no…
  10. 360.If the system of linear equations x - 4y + 7z = g 3y - 5z = h -2x + 5y - 9z = k is consist…
  11. 361.Let A = X = (x, y, z)T: PX = 0 and x2 + y2 + z2 = 1 where [P = [ pmatrix 1 & 2 & 1 - 2 & 3…
  12. 362.Let a, b, c [ ] R be all non-zero and satisfy a3 + b3 + c3 = 2.
  13. 363.Let S be the set of all [ ] [ ] R for which the system of linear equations 2x -- y + 2z = …
  14. 364.Let A be a 2 [ ] 2 real matrix with entries from 0, 1 and |A| [ ] 0.
  15. 365.Let A be a 3 [ ] 3 matrix such that adj A = [[ pmatrix 2 & - 1 & 1 - 1 & 0 & 2 1 & - 2 & -…
  16. 366.If the system of equations x+y+z=2 2x+4y--z=6 3x+2y+[ ]z=[ ] has infinitely many solutions…
  17. 367.If [A = [ pmatrix & i i & pmatrix ]], [( = 24 )] and [A^5 = [ pmatrix a & b c & d pmatrix …
  18. 368.If a + x = b + y = c + z + 1, where a, b, c, x, y, z are non-zero distinct real numbers, t…
  19. 369.Let [ ] R .
  20. 370.Let [ = 5] and [A = [ pmatrix & - & pmatrix ]].
  21. 371.The values of [ ] and [ ] for which the system of linear equations x + y + z = 2 x + 2y + …
  22. 372.If the system of linear equations 2x + 2ay + az = 0 2x + 3by + bz = 0 2x + 4cy + cz = 0, w…
  23. 373.The system of linear equations [ ]x + 2y + 2z = 5 2[ ]x + 3y + 5z = 8 4x + [ ]y + 6z = 10 …
  24. 374.If [A = ( pmatrix 2 & 2 9 & 4 pmatrix )] and [I = ( pmatrix 1 & 0 0 & 1 pmatrix )] then 10…
  25. 375.For which of the following ordered pairs ([ ], [ ]), the system of linear equations x + 2y…
  26. 376.If the matrices A = [[ pmatrix 1 & 1 & 2 1 & 3 & 4 1 & - 1 & 3 pmatrix ]], B = adjA and C …
  27. 377.If for some [ ] and [ ] in R, the intersection of the following three places x + 4y -- 2z …
  28. 378.Let [A = [ pmatrix i & - i - i & i pmatrix ],i = - 1 ].
  29. 379.If x, y, z are in arithmetic progression with common difference d, x [] 3d, and the determ…
  30. 380.The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k2 has no solution…
  31. 381.Let the system of linear equations 4x + []y + 2z = 0 2x - y + z = 0 []x + 2y + 3z = 0, [],…
  32. 382.Let [], [], [] be the real roots of the equation, x3 + ax2 + bx + c = 0, (a, b, c [] R and…
  33. 383.Let [A + 2B = [ pmatrix 1 & 2 & 0 6 & - 3 & 3 - 5 & 3 & 1 pmatrix ]] and [2A - B = [ pmatr…
  34. 384.Consider the system of linear equations -x + y + 2z = 0 3x - ay + 5z = 1 2x - 2y - az = 7 …
  35. 385.The value of k []R, for which the following system of linear equations 3x - y + 4z = 3, x …
  36. 386.The values of [] and [] such that the system of equations x + y + z = 6, 3x + 5y + 5z = 26…
  37. 387.Let A and B be 3 [] 3 real matrices such that A is symmetric matrix and B is skew-symmetri…
  38. 388.For the system of linear equations: [x - 2y = 1,x - y + kz = - 2,ky + 4z = 6,k R], conside…
  39. 389.The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9 x - y + 4z = 8
  40. 390.The number of distinct real roots of [| pmatrix x & x & x x & x & x x & x & x pmatrix | = …
  41. 391.The values of a and b, for which the system of equations 2x + 3y + 6z = 8 x + 2y + az = 5 …
  42. 392.Let [A = ( pmatrix 1 & 0 & 0 0 & 1 & 1 1 & 0 & 0 pmatrix )].
  43. 393.Consider the following system of equations : x + 2y - 3z = a 2x + 6y - 11z = b x - 2y + 7z…
  44. 394.Let [A = ( pmatrix [x + 1] & [x + 2] & [x + 3] [x] & [x + 3] & [x + 3] [x] & [x + 2] & [x …
  45. 395.Let A(a, 0), B(b, 2b + 1) and C(0, b), b [] 0, |b| [] 1, be points such that the area of t…
  46. 396.Let [[]] be the greatest integer less than or equal to [].
  47. 397.If the matrix [A = ( pmatrix 0 & 2 K & - 1 pmatrix )] satisfies A(A^3 + 3I) = 2I, then the…
  48. 398.Let A and B be two 3 [] 3 real matrices such that (A2 - B2) is invertible matrix.
  49. 399.If [] + [] + [] = 2[], then the system of equations x + (cos [])y + (cos [])z = 0 (cos [])…
  50. 400.If the following system of linear equations 2x + y + z = 5 x - y + z = 3 x + y + az = b ha…