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Matrices and Determinants

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  1. 201.Let A be a 33 matrix such that |adj(adj(adjA))|=12^4.
  2. 202.Let x,y,z>1 and [A=pmatrix1 & _xy & _xz _yx & 2 & _yz _zx & _zy & 3pmatrix.] Then adj(adj(…
  3. 203.Let A=pmatrix1√10 & 3√10 -3√10 & 1√10pmatrix and B=pmatrix1&-i0&1pmatrix, where i=-1.
  4. 204.Let A,B,C be 33 matrices such that A is symmetric and B,C are skew-symmetric.
  5. 205.Let , be real numbers.
  6. 206.The set of all values of tR for which the matrix [pmatrixe^t & e^-t( t-2 t) & e^-t(-2 t- t…
  7. 207.Let A be a symmetric matrix such that |A|=2 and A=pmatrix2/3 & 11 & 2pmatrix-type relation…
  8. 208.Let A=pmatrixm&n&qpmatrix, d=|A|0, and A-d(adjA)=O.
  9. 209.If P is a 33 real matrix such that P^T=aP+(a-1)I, where a>1, then
  10. 210.Let A=pmatrix1&0&00&4&-10&12&-3pmatrix.
  11. 211.Let A be an n n matrix such that |A|=2.
  12. 212.If A=12pmatrix1&√3-√3&1pmatrix, then:
  13. 213.Let A=[a_ij]_22, where a_ij0 for all i,j and A^2=I.
  14. 214.Let A=pmatrix2&1&01&2&-10&-1&2pmatrix.
  15. 215.Let P=pmatrix√32 & 12 -12 & √32pmatrix, A=pmatrix1&10&1pmatrix, and Q=PAP^T.
  16. 216.If A=pmatrix1&5&10pmatrix, A^-1= A+ I, and +=-2, then 4^2+^2+^2 is equal to:
  17. 217.If A=pmatrix15!6!7! & & 5!
  18. 218.Let A=pmatrix0&1&2&0&31&c&0pmatrix, where a,cR.
  19. 219.Let A=pmatrix1&1510&1pmatrix.
  20. 220.The number of symmetric matrices of order 3, with all the entries from the set 0,1,2,,9, i…
  21. 221.Let B=pmatrix1&3&1&2&3&&4pmatrix, >2, be the adjoint of a matrix A with |A|=2.
  22. 222.Let A=pmatrix1&2&3&3&11&1&2pmatrix, |A|=2.
  23. 223.Let the determinant of a square matrix A of order m be m-n, where m,n satisfy 4m+n=22 and …
  24. 224.Let S=A=pmatrix-1&a0&bpmatrix: a,b1,2,,100 and let T_n=A S: A^n(n+1)=I.
  25. 225.Let A be a 33 real matrix such that Apmatrix110pmatrix=pmatrix111pmatrix, Apmatrix101pmatr…
  26. 226.Let A=pmatrix0&-22&0pmatrix.
  27. 227.Let A be a 33 matrix having entries from the set -1,0,1.
  28. 228.Let A=pmatrix2&-21&-1pmatrix and B=pmatrix-1&2-1&2pmatrix.
  29. 229.Let A be a 33 invertible matrix.
  30. 230.Let X=pmatrix0&1&00&0&10&0&0pmatrix, Y= I+ X+ X^2, Z=^2I- X+(^2-)X^2, ,,R.
  31. 231.The positive value of the determinant of the matrix A, whose Adj(Adj(A))=pmatrix14&28&-14-…
  32. 232.Let A and B be two 33 matrices such that AB=I and |A|=18.
  33. 233.Let A be a matrix of order 22, whose entries are from the set 0,1,2,3,4,5.
  34. 234.Let A be a matrix of order 33 and (A)=2.
  35. 235.Let A=pmatrix1+i&1-i&0pmatrix where i=-1.
  36. 236.The probability that a randomly chosen 22 matrix with all entries from the set of first 10…
  37. 237.Let A=[a_ij] be a square matrix of order 3 such that a_ij=2^j-i for all i,j=1,2,3.
  38. 238.Let A=pmatrix2&-10&2pmatrix.
  39. 239.Let M=pmatrix0&-&0pmatrix, where is a non-zero real number, and N=_k=1^49M^2k.
  40. 240.Let S= n: 1 n50, n odd.
  41. 241.Let A=pmatrix2&-1&-11&0&-11&-1&0pmatrix and B=A-I.
  42. 242.Let A=pmatrix1&a&a0&1&b0&0&1pmatrix, a,bC.
  43. 243.Let A be a 22 matrix with (A)=-1 and ((A+I)(Adj(A)+I))=4.
  44. 244.Let A=pmatrix111pmatrix and B=pmatrix9^2&-10^2&11^212^2&13^2&-14^2-15^2&16^2&17^2pmatrix.
  45. 245.The number of matrices A=pmatrixa&b&dpmatrix, where a,b,c,d-1,0,1,2,3,,10, such that A=A^-…
  46. 246.Let A=pmatrix1&2-2&-5pmatrix.
  47. 247.Let S be the set containing all 33 matrices with entries from -1,0,1.
  48. 248.Let A=pmatrix4&-2&pmatrix.
  49. 249.Consider a matrix A=pmatrix&&^2&^2&^2+&+&+pmatrix, where ,, are three distinct natural num…
  50. 250.Let the matrix A=pmatrix0&1&00&0&11&0&0pmatrix and B_0=A^49+2A^98.