Home
Class 12
MATHS
Show that the following system of equati...

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

Text Solution

Verified by Experts

We have given
`2x-y+3z=5`,
`3x+2y-z=7` ,
`4x+5y-5z=0`
We can write them in matrix from AX=B....(i)
`⇒[(2,-1,3),(3,2,-1),(4,5,-5)][(x),(y),(z)]=[(5),(7),(0)]`
Determinant of matrix A,
`|A∣=|(2,-1,3),(3,2,-1),(4,5,-5)|`
...
Promotional Banner

Topper's Solved these Questions

  • SCALAR TRIPLE PRODUCT

    RD SHARMA|Exercise Solved Examples And Exercises|59 Videos

  • STRAIGHT LINE IN SPACE

    RD SHARMA|Exercise Solved Examples And Exercises|134 Videos

Similar Questions

Explore conceptually related problems

Use matrix method to show that the following system of equation is inconsistent 3x-y+2z=3 2x+y+3z=5 x-2y-z=1

Using matrix method, show that following system of equation is inconsistent : 2x+3y-z+4=0 x-y+2z-7=0 x+4y-3z+5=0

Show that following system of linear equations is inconsistent: 4x-5y-2z=2,\ \ 5x-4y+2z=-2,\ \ 2x+2y+8z=-1

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

Show that the following systems of linear equations are inconsistent: 3x-y+2z=3,\ \ 2x+y+3z=5,\ \ x-2y-z=1

Solve the following system of equations: 2x-3y+5z=11, 5x+2y-7z=-12, -4x+3y+z=5

Using matrices,solve the following system of equations: 3x-y+z=5 ,2x-2y+3z=7,x+y-z=-1

Show that each of the following systems of linear equations is consistent and also find their solutions: 6x+4y=2 9x+6y=3 2x+3y=5 6x+9y=15 5x+3y+7z=4 3x+26 y+2z=9 7x+2y+10 z=5 x-y+z=3 2x+y-z=2 -x-2y+2z=1 x+y+z=6 x+2y+3z=14 x+4y+7z=30 2x+2y-2z=1 4x+4y-z=2 6x+6y+2z=3

Using matrices,solve the following system of equations: 2x-3y+5z=11,3x+2y-4z=-5,x+y-2z=-3

Using matrices, solve the following system of equations for x,y and z. 2x+3y+3z=5 , x-2y+z=-4 , 3x-y-2z=3

RD SHARMA-SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS-Solved Examples And Exercises
  1. Solve the following system of equations, using matrix method. x+2y+z=7...

    Text Solution

    |

  2. Use matrix method to examine the following system of equations for con...

    Text Solution

    |

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

    Text Solution

    |

  4. If A=[(1,2, 1), (-1, 1,1), (1, -3, 1)], find A^(-1) and hence solve th...

    Text Solution

    |

  5. If A=[(1,2,-3),(2,3,2),(3,-3,-4)] then find A^-1 and hence solve the f...

    Text Solution

    |

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

    Text Solution

    |

  7. An amount of Rs 5000 is put into three investments at the rate of inte...

    Text Solution

    |

  8. Solve the following system of equations by matrix method: 5x+7y+2=0...

    Text Solution

    |

  9. Solve the following system of equations by matrix method: 5x+2y=3,\...

    Text Solution

    |

  10. Solve the following system of equations by matrix method: 3x+4y-5=0,...

    Text Solution

    |

  11. Solve the following system of equations by matrix method: 3x+y=19 ,...

    Text Solution

    |

  12. Solve the following system of equations by matrix method: 3x+7y=4,\...

    Text Solution

    |

  13. Solve the following system of equations by matrix method: 3x+y=7,\ ...

    Text Solution

    |

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

    Text Solution

    |

  15. Solve the following system of equations by matrix method: x+y+z=3,\...

    Text Solution

    |

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

    Text Solution

    |

  17. Using matrix method, solve the following system of linear equations. 3...

    Text Solution

    |

  18. Using matrix method, solve the following system of equations: 2/x+...

    Text Solution

    |

  19. Using matrices, solve the following system of linear equations: x\...

    Text Solution

    |

  20. Show that each of the following systems of linear equations is cons...

    Text Solution

    |