Home
Class 12
MATHS
Using the properties of determinants pro...

Using the properties of determinants prove that
`|{:(a+b+2c,a,b),(c,b+c+2a,b),(c,a,c+a+2b):}|=2(a+b+c)^3` or `|{:(x+y+2z,x,y),(z,y+z+2x,y),(z,x,z+x+2y):}|=2(x+y+z)^3`

Promotional Banner

Topper's Solved these Questions

  • MODEL QUESTION PAPER -16

    SHARAM PUBLICATION|Exercise EXERCISE|45 Videos

  • MODEL QUESTION PAPER 12

    SHARAM PUBLICATION|Exercise EXERCISE|41 Videos

Similar Questions

Explore conceptually related problems

Using properties of determinants prove that |{:(a+x,y,z),(x,a+y,z),(x,y,a+z):}|=a^2 (a+x+y+z)

Using properties of determinants, prove that |{:(y^2z^2,yz,y+z),(z^2x^2,zx,z+x),(x^2y^2,xy,x+y):}|=0

using the properties of determinants prove that |{:(1,x+y,x^2+y^2),(1,y+z,y^2+z^2),(1,z+x,z^2+x^2):}|=(x-y)(y-z)(z-x)

Using properties of the determinants, prove that: |[2y, y-z-x, 2y],[2z, 2z, z-x-y], [x-y-z, 2x, 2x]| = (x+y+z)^3

Show that |{:(a,b,c),(a+2x,b+2y,c+2z),(x,y,z):}|=0

Without expanding show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+c):}|=0

Without expanding , show that |{:(x,a,x+a),(y,b,y+b),(z,c,z+a):}|=0

Prove that: |[y+z, z, y],[z, z+x, x], [y, x, x+y]|= 4 xyz

Show that: |[(y+z)^2, xy, zx],[xy, (x+z)^2, yz], [xz, yz, (x+y)^2]|=2xyz(x+y+z)^3

SHARAM PUBLICATION-MODEL QUESTION PAPER -17-EXERCISE
  1. Find the transpose of the matrix [[3,-2,-4],[3,-2,-5],[-1,1,2]].

    Text Solution

    |

  2. Prove the following: [[b^2-ab,b-c,bc-ac],[ab-a^2,a-b,b^2-ab],[bc-ac,...

    Text Solution

    |

  3. Using the properties of determinants prove that |{:(a+b+2c,a,b),(c,b...

    Text Solution

    |

  4. Evaluate int(x+sqrt(x^2+a^2))dx

    Text Solution

    |

  5. Evaluate intcosec^2xsqrt(cotx)dx

    Text Solution

    |

  6. Prove that int0^(pi/2)lnSinxdx=-pi/2ln2

    Text Solution

    |

  7. Determine the area of the region between the curves y=cosx and y=sinx,...

    Text Solution

    |

  8. Find the general solution of the differential equation (1+x^2) tan^-1y...

    Text Solution

    |

  9. Prove that f:RrightarrowR such that f(x)=frac[2x^2][x^2+1] is neither ...

    Text Solution

    |

  10. Let A={1, 2, 3, 5}, B={4, 6, 9}, A relation R form A to B is defined b...

    Text Solution

    |

  11. Consider the binary operation ** on the set {1, 2, 3, 4 5} defined by ...

    Text Solution

    |

  12. Prove statement tan ( 2 "tan"^(-1)1/5-pi/4) + 7/17 =0

    Text Solution

    |

  13. Find the maixmum value of z =50x1+60x2 subject to 2x1+3x2le6,x1,x2ge0

    Text Solution

    |

  14. Write the values of a and b, for which the vectors (a-1)hat(i) + (b+2)...

    Text Solution

    |

  15. Find the scalar projection of the vector veca = 3hati+6hatj + 9hatk on...

    Text Solution

    |

  16. Find the co-ordinates of the point where the perpendicular from the or...

    Text Solution

    |

  17. Find the equation of the plane passing through the line x = y = z and ...

    Text Solution

    |

  18. Find the co-ordinates of the point where the line (x-2)/3=(y+1)/4=(z-2...

    Text Solution

    |

  19. Find (dy)/(dx) when x^y+y^x=a^b

    Text Solution

    |

  20. Evaluate inte^x((1+sinx)/(1+cosx))dx.

    Text Solution

    |