Home
Class 12
MATHS
If |{:(a,b,0),(0,a,b),(b,0,a):}|=0, then...

If `|{:(a,b,0),(0,a,b),(b,0,a):}|=0`, then which one of the following is correct ?

A

`(a)/(b) is one of the cube roots of unity.

B

`(a)/(b)` is one of the cube roots of -1.

C

a is one of the cube roots of unity.

D

b is one of the cube roots of unity.

Text Solution

Verified by Experts

The correct Answer is:
B
`|(a,b,0),(0,a,b),(b,0,a)|`
`=a[a^(2)-0]-b[-b^(2)]+0`
`=a^(3)+b^(3)=0`
`rArr a^(3)=-b^(3)`
`rArr ((a)/(b))^(3)=-1`
Hence, `(a)/(b)` is one of the cube roots of `-1`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    NDA PREVIOUS YEARS|Exercise MCQ|59 Videos

  • PAIR OF STRAIGHT LINES

    NDA PREVIOUS YEARS|Exercise Example|12 Videos

Similar Questions

Explore conceptually related problems

If det[[a,b,00,a,bb,0,a]]=0, then which one of the

If |{:(a,b,0),(0,a,b),(b,0,a):}| = 0, (a ne 0 ) then

If A=[{:(0,1),(-1,0)],B=[{:(i,0),(0,-i):}],C=[{:(0,-i),(-i,0):}] , then which one of the following in not correct ?

If A =({:(i,0),(0,-i):}),B=({:(0,-1),(1,0):}),C=({:(0,i),(i,0):}) wher i = sqrt(-1) , then which one of the following is correct ?

If A=[{:(0,1),(-1,0):}] B=[{:(i,0),(0,-i):}] C=[{:(0,-i),(-i,0):}] then which one of the following is not correct ?

If A[{:(i,0),(0,-i)]B=[{:(0,-1),(1,0)] and C =[{:(0,i),(i,0):}] where i= sqrt(-1) . Then which one of the following is correct ?

If the sum of the squares of the distances of the point (x, y) from the points (a, 0) and (-a, 0) is 2b^(2) , then which one of the following is correct ?

If the sum of the squares of the distances of the point (x, y) from the points (a, 0) and (-a,0) is 2b^(2) , then which one of the following is correct ?

NDA PREVIOUS YEARS-MATRICES & DETERMINANTS-MQS
  1. From the matrix equation AB = AC we can conclude B = C provided that

    Text Solution

    |

  2. If {:A=[(4,x+2),(2x-3,x+1)]:} is symmetric, then x =

    Text Solution

    |

  3. If |{:(a,b,0),(0,a,b),(b,0,a):}|=0, then which one of the following is...

    Text Solution

    |

  4. If A and B are square matrices of order 3 such that absA=-1,absB=3," t...

    Text Solution

    |

  5. Which one of the following matrices is an elementary matrix ?

    Text Solution

    |

  6. If A=[{:(2,7),(1,5):}] then that is A + 3A^(-1) equal to ?

    Text Solution

    |

  7. The matrix [{:(" "0,-4+i),(4+I," "0):}] is

    Text Solution

    |

  8. Consider the following in respect of two non-singular matrices A and B...

    Text Solution

    |

  9. If X=[{:(3,-4),(1,-1):}],B=[{:(5,2),(-2,1):}]and A=[{:(p,q),(r,s):}] s...

    Text Solution

    |

  10. A=[(x+y,y),(2x,x-y)] B=[(2),(-1)]and C = [(3),(2)] If AB = C, th...

    Text Solution

    |

  11. The value of |{:(1," "1," "1),(1,1+x," "1),(1," "1,1+y):}|is

    Text Solution

    |

  12. If E(theta)=[[cos theta, sin theta] , [-sin theta, cos theta]] then E(...

    Text Solution

    |

  13. The matrix A=[[1,3,2],[1,x-1,1],[2,7,x-3]] will have inverse for every...

    Text Solution

    |

  14. If the value of the determinants |(a,1,1),(1,b,1),(1,1,c)| is positive...

    Text Solution

    |

  15. Consider the following statements in respect of the determinant |[cos^...

    Text Solution

    |

  16. If A=[{:(1,0,-2),(2,-3,4):}], then the matrix X for which 2X + 3A = 0 ...

    Text Solution

    |

  17. If A=[{:(1,1,-1),(2,-3,4),(3,-2,3):}]and B=[{:(-1,-2,-1),(6,12,6),(5,1...

    Text Solution

    |

  18. If A is an invertible matrix of order n and k is any positive real num...

    Text Solution

    |

  19. If A is an orthogonal matrix of order 3 and B = [{:(1,2,3),(-3,0,2),(2...

    Text Solution

    |

  20. If a, b, c are real numbers, then the value the determinant |(1-a,a-...

    Text Solution

    |