Home
Class 12
MATHS
If a, b and c are real numbers, and Delt...

If a, b and c are real numbers, and `Delta=|b+cc+a a+b c+a a+bb+c a+bb+cc+a|=0` .Show that either `a" "+" "b" "+" "c" "=" "0" "or" "a" "=" "b" "=" "c` .

Text Solution

Verified by Experts

Given `Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|`
Applying `R_1->R_1+R_2+R_3`
`=|[2(a+b+c) , 2(a+b+c) , 2(a+b+c)],[c+a, a+b , b+c],[a+b , b+c ,c+a]|`
Taking common `2(a+b+c)` from `R_1`
...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.7|17 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos

Similar Questions

Explore conceptually related problems

If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0 . Show that either a+b+c=0 or a=b=c

If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,b+c),(a+b,b+c,c+a)|=0 , then show that either a+b+c=0 or, a=b=c .

If a ,b , c are nonzero real numbers such that |b cc a a b c a a bb c a bb cc a|=0,t h e n 1/a+1/(bomega)+1/(comega^2)=0 b. 1/a+1/(bomega^2)+1/(comega^)=0 c. 1/(aomega)+1/(bomega^2)+1/c=0 d. none of these

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x 3

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x >3.

Let a ,b ,and c be real numbers such that 4a+2b+c=0 and a b > 0. Then the equation a x^2+b x+c = 0

If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c 0 (c) a >0

If x, a, b, c are real and (x-a+b)^(2)+(x-b+c)^(2)=0 , then a, b, c are in

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

If a, b, c are distinct real numbers, show that the points (a, a^2), (b, b^2) and (c, c^2) are not collinear.

NCERT ENGLISH-DETERMINANTS-All Questions
  1. Without expanding the determinant, prove that |(a,a^2,bc),(b,b^2,ca),(...

    Text Solution

    |

  2. Evaluate |(cosalphacosbeta,cosalpha sinbeta , - sin alpha),(-sin beta,...

    Text Solution

    |

  3. If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+...

    Text Solution

    |

  4. Solve the equation |(x+a, x,x),(x,x+a, x),(x,x,x+a)|=0, a!= 0

    Text Solution

    |

  5. Prove: |a^2b c a c+c^2a^2+a bb^2a c a bb^2+b cc^2|=4a^2b^2c^2

    Text Solution

    |

  6. Solve system of linear equations, using matrix method, 2x+y+z=1" "x-2...

    Text Solution

    |

  7. Solve system of linear equations, using matrix method, x - y + z = 4"...

    Text Solution

    |

  8. The sum of three numbers is 6. If multiply theird number by 3 and add ...

    Text Solution

    |

  9. Solve the following system of equations by matrix method. 3x-2y + 3z=...

    Text Solution

    |

  10. Solve the system of equations2x + 5y = 1 and 3x + 2y = 7

    Text Solution

    |

  11. Show that the matrix A=[2 3 1 2]satisfies the equation A^2-4A+I=0

    Text Solution

    |

  12. If A=[[2,3],[1,-4]]and B=[[1,-2],[-1,3]], then verify that (A B)^(-1)=...

    Text Solution

    |

  13. If A=[[1 ,3 ,3],[ 1, 4 ,3],[ 1, 3, 4]],then verify thatA a d j A = |A|...

    Text Solution

    |

  14. Find adj for A=[[2 , 3 ] , [1 , 4]]

    Text Solution

    |

  15. Find minors and cofactors of the elements of the determinant|2-3 5 6 ...

    Text Solution

    |

  16. Find minors and cofactors of the elements a(11), a(21)in the determin...

    Text Solution

    |

  17. Find minors and cofactors of all the elements of the determinant |[1,...

    Text Solution

    |

  18. Using the property of determinants and without expanding, prove that:...

    Text Solution

    |

  19. Using the property of determinants and without expanding, prove that:...

    Text Solution

    |

  20. Using the property of determinants and without expanding, prove that:...

    Text Solution

    |