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Matrices and Determinants

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  1. 301.The matrix A^2+4A-5I, where I is the identity matrix and A=pmatrix1&24&-3pmatrix, equals:
  2. 302.If A=pmatrix-100pmatrix, B=pmatrix+100pmatrix are two (column) matrices, then AB^T is a no…
  3. 303.If A=pmatrix1&0&02&1&0-3&2&1pmatrix and B=pmatrix1&0&0-2&1&07&-2&1pmatrix, then AB equals
  4. 304.If 1 is the complex cube root of unity and matrix H=pmatrix&00&pmatrix, then H^70 is equal…
  5. 305.Let A and B be two symmetric matrices of order 3.
  6. 306.The number of 33 non-singular matrices, with four entries as 1 and all other entries as 0,…
  7. 307.Let A=pmatrix1&23&4pmatrix and B=pmatrixa&00&bpmatrix, a,bN.
  8. 308.If A and B are square matrices of size n n such that A^2-B^2=(A-B)(A+B), then which of the…
  9. 309.If A=pmatrix1&01&1pmatrix and I=pmatrix1&00&1pmatrix, then which one of the following hold…
  10. 310.If A=pmatrixa&b&apmatrix and A^2=pmatrix&&pmatrix, then:
  11. 311.If the system of linear equations x + 2ay + az = 0; [x + 3by + bz = 0;,,x + 4cy + cz = 0;]…
  12. 312.Let [A = ( pmatrix 1 & - 1 & 1 2 & 1 & - 3 1 & 1 & 1 pmatrix ).] and 10 [B = ( pmatrix 4 &…
  13. 313.Let [A = ( pmatrix 0 & 0 & - 1 0 & - 1 & 0 - 1 & 0 & 0 pmatrix )].
  14. 314.If A^2 - A + 1 = 0, then the inverse of A is :
  15. 315.The system of equations [pmatrix ,x + y + z = - 1 x + y + z = - 1 x + y + ,z = - 1 pmatrix…
  16. 316.Let [A = ( pmatrix 1 & 2 3 & 4 pmatrix )] and [B = ( pmatrix a & 0 0 & b pmatrix ),a,b N.]…
  17. 317.Let [A = | pmatrix 5 & 5 & 0 & & 5 0 & 0 & 5 pmatrix |.] If [,,| A^2 | = 25,] then [,| |] …
  18. 318.If [D = | pmatrix 1 & 1 & 1 1 & 1 + x & 1 1 & 1 & 1 + y pmatrix |] for [x 0,y 0,] then D i…
  19. 319.Let A be [a,2 2] matrix with real entries.
  20. 320.Let a, b, c be any real numbers.
  21. 321.Let A be a square matrix all of whose entries are integers.
  22. 322.Let A be a [,2 2] matrix Statement - 1 : [adj( adj,A ) = A] Statement - 2 :[| adj,A | = | …
  23. 323.The number of values of k for which the linear equations 4x + ky + 2z = 0,kx + 4y + z = 0 …
  24. 324.Let [A = ( pmatrix 1 & 0 & 0 2 & 1 & 0 3 & 2 & 1 pmatrix )].
  25. 325.Let P and Q be [3 3] matrices [P Q.] If P^3 = Q^3 and P^2Q = Q^2P then determinant of [( P…
  26. 326.If [P = [ pmatrix 1 & & 3 1 & 3 & 3 2 & 4 & 4 pmatrix ]] is the adjoint of a [3 3] matrix …
  27. 327.If A is a [3 3] non-singular matrix such that AA'=A'A and B = A^ - 1A', then BB' equals:
  28. 328.The system of linear equations [pmatrix x + y - z = 0 x - y - z = 0 x + y - z = 0 pmatrix …
  29. 329.If [A = [ pmatrix 5a & - b 3 & 2 pmatrix ]] and A adj A=A A^T, then 5a+b is equal to :
  30. 330.If A = [[ pmatrix - 4 & - 1 3 & 1 pmatrix ]], then the determinant of the matrix (A2016 - …
  31. 331.Let A be a 3 [ ] 3 matrix such that A2 - 5A + 7I = 0 Statement - I : A-1 = [1 7] (5I - A).
  32. 332.The number of distinct real roots of the equation, [| pmatrix x & x & x x & x & x x & x & …
  33. 333.If [A = [ pmatrix 2 & - 3 - 4 & 1 pmatrix ]], then adj(3A2 + 12A) is equal to
  34. 334.If S is the set of distinct values of 'b' for which the following system of linear equatio…
  35. 335.If [S = x [ 0,2 ]:| pmatrix 0 & x & - x x & 0 & x x & x & 0 pmatrix | = 0 ,] then [_x S ( …
  36. 336.The number of real values of [ ] for which the system of linear equations 2x + 4y - [ ]z =…
  37. 337.Let A be any 3 [ ] 3 invertible matrix.
  38. 338.For two 3 3 matrices A and B, let A + B = 2BT and 3A + 2B = I3, where BT is the transpose …
  39. 339.If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a …
  40. 340.Suppose A is any 3[ ] 3 non-singular matrix and ( A - 3I) (A - 5I) = O where I = I3 and O …
  41. 341.If the system of linear equations x + ay + z = 3 x + 2y + 2z = 6 x + 5y + 3z = b has no so…
  42. 342.Let S be the set of all real values of k for which the systemof linear equations x + y + z…
  43. 343.The number of values of k for which the system of linear equations, (k + 2)x + 10y = k kx …
  44. 344.Let [ ] be a real number for which the system of linear equations x + y + z = 6, 4x + [ ]y…
  45. 345.The sum of the real roots of the equation [| pmatrix x & - 6 & - 1 2 & - 3x & x - 3 - 3 & …
  46. 346.If [ _1 = | pmatrix x & & - & - x & 1 & 1 & x pmatrix |] and [ _2 = | pmatrix x & 2 & 2 - …
  47. 347.If the system of linear equations x + y + z = 5 x + 2y + 2z = 6 x + 3y + [ ]z = [ ], ([ ],…
  48. 348.The number of values of [ ] [ ] (0, [ ]) for which the system of linear equations x + 3y +…
  49. 349.Let A and B be two invertible matrices of order 3 [ ] 3.
  50. 350.If the system of linear equations 2x + 2y + 3z = a 3x -- y + 5z = b x -- 3y + 2z = c where…