Home
Class 11
MATHS
If P=[1alpha3 1 3 3 2 4 4] is the adjo...

If `P=[1alpha3 1 3 3 2 4 4]` is the adjoint of a `3xx3` matrix A and `|A|""=""4` , then a is equal to (1) 11 (2) 5 (3) 0 (4) 4

A

4

B

11

C

5

D

10

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `{:P=[(1,a,3),(1,3,3),(2,4,4)]:}`
`:. absP =(12-12)-a(4-6)+3(4-6)=2a-6`
We have, adj A =P
`rArrabs(adjA)=absP`
`rArrabs(A)^(3-1)=2a-6[ :' abs(adjA)=abs(A)^(n-1)]`
`rArr 4^2=2a-6rArr a=11`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Solved Mcqs|57 Videos

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Assertion Reason Type|12 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

If P=[(1,alpha,3),(1,3,3),(2,4,4)] is the adjoint of a 3 x 3 matrix A and |A| = 4 , then alpha is equal to

If A is 3xx3 matrix and |A|=4 , then |A^(-1)| is equal to

If A=[(1,x,3),(1,3,3),(2,4,4)] is the adjoint of a 3xx3 matrix B and det. (B)=4 , then the value of x is ______ .

1.Find the adjoint of the matrix A= [[1,2],[3,4]]

Write the adjoint of the matrix A=[(-3, 4),(7,-2)] .

find the adjoint of the matrix A=[(1,2,3),(0,5,0),(2,4,3)]

Let A=[(1, 2), (3,-5)] and B=[(1, 0), (0, 2)] and X be a matrix such that A=B X , then X is equal to (a) 1/2[(2, 4), (3, -5)] (b) 1/2[(-2, 4), (3, 5)] (c) [(2, 4), (3,-5)] (d) none of these

Find adjoint of the matrice in [(1, 2),( 3, 4)]

If A = [[0 , 1, -1],[4, -3, 4],[3, -3, 4]] find the transpose of A matrix

Write the adjoint of the following matrix: [[2,-1],[4,3]]

OBJECTIVE RD SHARMA ENGLISH-MATRICES-Chapter Test
  1. If P=[1alpha3 1 3 3 2 4 4] is the adjoint of a 3xx3 matrix A and ...

    Text Solution

    |

  2. If A is an invertible matrix and B is a matrix, then

    Text Solution

    |

  3. What is the order of the product [x" "y" "z][{:(a,h,g),(h,b,f),(g,f,c)...

    Text Solution

    |

  4. If {:A=[(a,0,0),(0,b,0),(0,0,c)]:}," then "A^(-1), is

    Text Solution

    |

  5. The inverse of the matrix {:[(1,3),(3,10)]:} is equal to

    Text Solution

    |

  6. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

    Text Solution

    |

  7. If {:X=[(3,-4),(1,-1)]:}, the value of X^n is equal to

    Text Solution

    |

  8. If {:A=[(5,2),(3,1)]:}," then "A^(-1)=

    Text Solution

    |

  9. For the system of equations: x+2y+3z=1 2x+y+3z=2 5x+5y+9z=4

    Text Solution

    |

  10. If {:A=[(3,1),(-1,2)]:}," then "A^(2)=

    Text Solution

    |

  11. if A=[(4,x+2),(2x-3,x+1)] is symmetric, then x is equal to

    Text Solution

    |

  12. If A+B={:[(1,0),(1,1)]:}andA-2B={:[(-1,1),(0,-1)]:}, then A is equal t...

    Text Solution

    |

  13. {:[(-6,5),(-7,6)]^(-1)=:}

    Text Solution

    |

  14. From the matrix equation AB=AC, we conclude B=C provided.

    Text Solution

    |

  15. If I3 is the identily matrix of order 3, then (I3)^(-1)=

    Text Solution

    |

  16. Let a ,b , c be real numbers. The following system of equations in x ,...

    Text Solution

    |

  17. If A and B are two matrices such that A+B and AB are both defind, then

    Text Solution

    |

  18. A and B are tow square matrices of same order and A' denotes the tran...

    Text Solution

    |

  19. STATEMENT-1: The lines a(1)x+b(1)y+c(1)=0a(2)x+b(2)y+c(2)=0,a(3)x+b(3)...

    Text Solution

    |

  20. The system of linear equations x+y+z=2,2x+y-z=3, 3x+2y+kz=4 has a uniq...

    Text Solution

    |

  21. If A and B ar square matrices of order 3 such that |A|=-1|B|=3, then |...

    Text Solution

    |