Home
Class 12
MATHS
Let P = [[3, -1, -2],[2 ,0 ,alpha ],[3, ...

Let `P = [[3, -1, -2],[2 ,0 ,alpha ],[3, -5, 0]]`, where `alpha in R.` Suppose ` Q = [q_(ij) ] `is a
matrix such that `PQ= KI,` where `k in R, k ne 0 and I` is the
identity matrix of order 3. If
`q_(23) = - k/8`and `det. (Q) = k^(2)/2,` then

A

`alpha=0,k=8`

B

`4alpha-k+8=0`

C

`det(P adj(Q)) = 2^9`

D

`det(Q adj(P))=2^13`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    MODERN PUBLICATION|Exercise EXERCISE|326 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    MODERN PUBLICATION|Exercise EXERCISE|588 Videos

  • EXCLUSIVELY FOR JEE(ADVANCED)

    MODERN PUBLICATION|Exercise EXERCISE|38 Videos

Similar Questions

Explore conceptually related problems

Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[q_(ij)] is a matrix such that PQ=kI, where k in RR, k != 0 and I is the identity matrix of order 3. If q_23=-k/8 and det(Q)=k^2/2, then

If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an identity matrix, prove theat det (M-I)=0.

If A is a square matrix of order 3 and I is an ldentity matrix of order 3 such that A^(3) - 2A^(2) - A + 2l =0, then A is equal to

Let P = {:[(1,0,0),(4,1,0),(16,4,1)] and I be te identity matrix of order 3. If Q = [q_(ij)] is A matrix such that P(50)-Q=I is then q31+q32/q21. The value of

Find the value of x such that PQ = QR, where P, Q and R are (6,- 1), (1, 3) and (x, 8) respectively.

If P is a 3xx3 matrix such that P^T = 2P+I , where P^T is the transpose of P and I is the 3xx3 identity matrix, then there exists a column matrix, X = [[x],[y],[z]]!=[[0],[0],[0]] such that

Let P=[(1,0,0),(3,1,0),(9,3,1)] and Q = [q_(ij)] be two 3xx3 matrices such that Q - P^(5) = I_(3) . Then (q_(21)+q_(31))/(q_(32)) is equal to

If A = [[0,-tan alpha/2],[tan alpha/2,0]] and I is the identity matrix of order 2, show that I + A = (I - A)[[cos alpha,-sin alpha],[sin alpha,cos alpha]]

For the matrix ( A=[[-3,6,0],[4,-5,8],[0,-7,-2]] ), find ( 1/2(A-A') ), where A' is the transpose of matrix A.

fill the blanks: if P is a matrix of order 2×4 and Q is of 4×3 then order of (PQ)' is __________.

MODERN PUBLICATION-DETERMINANTS-EXERCISE
  1. Without expanding show that following : |[a,a+b,a+b+c],[2a,3a+2b,4a+3b...

    Text Solution

    |

  2. If A = [[2,-3,5],[3,2,-4],[1,1,-2]] find A^-1. Using A^-1 solve the s...

    Text Solution

    |

  3. Let P = [[3, -1, -2],[2 ,0 ,alpha ],[3, -5, 0]], where alpha in R. Sup...

    Text Solution

    |

  4. Let M be a 2xx2 symmetric matrix with integer entries. Then , M is i...

    Text Solution

    |

  5. Let M and n be two 3xx3 matrices such that MN = NM. Further, If Mne ...

    Text Solution

    |

  6. For 3xx3 martrices M and N, which of the following statement (s) is ...

    Text Solution

    |

  7. If the adjoint of a 3x3 matrix P is (1 4 4) (2 1 7) (1 1 3) , t...

    Text Solution

    |

  8. If A is a matrix of order mxx m such that A^(2) +A + 2I = O, then

    Text Solution

    |

  9. Let a, b, and c be three real numbers satisfying [(a,b,c)][[1,9,7],[...

    Text Solution

    |

  10. Let omega be a solution of z^3-1 = 0 If a = 2 , b=8 and c =7 then the ...

    Text Solution

    |

  11. If A= ((1,0,0),(2,1,0),(3,2,1)), U(1), U(2), and U(3) are column matri...

    Text Solution

    |

  12. A complex number U = 4+2i.The value of |U| is

    Text Solution

    |

  13. Let A be the set of all 3× 3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  14. Let A be the set of all 3xx3 symmetric matrices all of whoes entries...

    Text Solution

    |

  15. For a 2xx2 matrix, A = [a(ij)], whose elements are given by a(ij) = ...

    Text Solution

    |

  16. If A is a square matrix such that A^2 = A, then write the value of (I+...

    Text Solution

    |

  17. Evaluate the following determinants: {:|(3,x),(x,1)| = |(3,2),(4,1)|

    Text Solution

    |

  18. If Delta={:|(1,2,3),(2,0,1),(5,3,8)|, write the minor of the element a...

    Text Solution

    |

  19. If A = [[3,1],[-1,2]], show thatA^2-5A +7I = O

    Text Solution

    |

  20. If A = [[costheta,sintheta],[-sintheta,costheta]] then prove that A^n...

    Text Solution

    |