Home
Class 12
MATHS
For what values of a and b , the followi...

For what values of `a` and `b` , the following system of equations is consistent?
`x+y+z=6`
`2x+5y+a z=b`
`x+2y+3z=14`

Text Solution

AI Generated Solution

To determine the values of \( a \) and \( b \) for which the following system of equations is consistent: 1. \( x + y + z = 6 \) 2. \( 2x + 5y + az = b \) 3. \( x + 2y + 3z = 14 \) we need to analyze the system using determinants. ...
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

  • DIFFERENTIABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|136 Videos

Similar Questions

Explore conceptually related problems

Show that the following system of equation is consistent.2x-y+3z=5,3x+2y-z=7,4x+5y-5z=0

Show that the following system of equations is consistent.x-y+z=3,2x+y-z=2,-x-2y+2z=1 Also,find the solution.

The value of x, y, z for the following system of equations x + y + z = 6, x - y + 2z = 5, 2x + y - z = 1 are

Show that the following systems of linear equations are inconsistent: 3x-y+2z=6,\ \ 2x-y+z=2,\ \ 3x+6y+5z=20.

For what value of k the following system of linear equations wil have infinite solutions x-y+z=3, 2x+y-z=2 and -3x-2ky+6z=3

For what values of p and q are the system of equations : 2x+5y+pz=q;x+2y+3z=14x+y+z=6 are consistent?

For what values of a and b the system of equations 2 x + ay + 6 z = 8 x+2y+bz=5 x + y + 3 z = 4 , has a unique solution ?

Use matrix to solve the following system of equations. x+y+z=6 x-y+z=2 2x+y-z=1

Using matrices,solve the following system of equations: x-y+z=4;2x+y-3z=0;x+y+z=2

RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If f(x)=a x^2+b x+c is a quadratic function such that f(1)=8,f(2)=11 a...

    Text Solution

    |

  2. The sum of three numbers is 6. If we multiply the third number 2 and ...

    Text Solution

    |

  3. For what values of a and b , the following system of equations is cons...

    Text Solution

    |

  4. Determine the values of lambda for which the following system of equa...

    Text Solution

    |

  5. Using determinants, show that the following system of linear equation ...

    Text Solution

    |

  6. By using determinants, solve the following system of equations: x+y+z=...

    Text Solution

    |

  7. Solve the following system of equations by using determinants: x+y+z=1...

    Text Solution

    |

  8. Using Cramers rule, solve the following system of linear equations: (...

    Text Solution

    |

  9. If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x...

    Text Solution

    |

  10. The value of |1 1 1^n C1^(n+2)C1^(n+4)C1^n C2^(n+2)C2^(n+4)C2| is

    Text Solution

    |

  11. Solve the following system of homogeneous equations: x+y-z=0 x-2y+...

    Text Solution

    |

  12. For what values of aa n db , the system of equations 2x+a y+6z=8 x+2y...

    Text Solution

    |

  13. If x , y , z are different from zero and |[1+x,1, 1],[1 , 1+y ,1],[ 1...

    Text Solution

    |

  14. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

    Text Solution

    |

  15. If [] denotes the greatest integer less than or equal to the real numb...

    Text Solution

    |

  16. L e t|3y x1|=|3 2 4 1| . Find possible values of xa n dy are natural n...

    Text Solution

    |

  17. If |[x-2,-3],[3x,2x]|=3 find the value of x

    Text Solution

    |

  18. Let A=|1sintheta1-sintheta1sintheta-1-sintheta1|, where 0lt=thetalt=2p...

    Text Solution

    |

  19. Find the minors of cofactors of elements of the matrix A=[a(i j)]=[[1,...

    Text Solution

    |

  20. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by two methods

    Text Solution

    |