Home
Class 12
MATHS
prove that abs[[a,b,c],[a+2x,b+2y,c+2z]...

prove that `abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0`

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    MAXIMUM PUBLICATION|Exercise EXAMPLE|119 Videos
  • PROBABILITY

    MAXIMUM PUBLICATION|Exercise EXAMPLE|144 Videos

Similar Questions

Explore conceptually related problems

Without expanding prove that abs[[x+y,y+z,z+x],[z,x,y],[1,1,1]]=0

Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

Find the values of x, y, z , if the matrix A=[[0, 2 y, z],[ x, y, -z],[ x, -y, z]] satisfy the equation A^' A=I

By using properties of determinants, prove that |[x+y+2z,x,y],[z,y+z+2x,y],[z,x,z+x+2y]|=2(x+y+z)^3

By using properties of determinants, prove that |[x,x^2,yz],[y,y^2,zx],[z,z^2,xy]|=(x-y)(y-z)(z-x)(xy+yz+zx)

Without expanding the determinant prove the following. |[x,a,x+a],[y,b,y+b],[z,c,z+c]|=0

If x + y + z = 0 , prove that |(ax,by,cz),(cy,az,bx),(bz,cx,ay)|=xyz|(a,b,c),(c,a,b),(b,c,a)|

Show that Delta=|[(y+z)^2, x y , z x],[ x y, (x+z)^2, y z],[ x z, y z, (x+y)^2]|=2 x y z(x+y+z)^3

Consider the determinant Delta=abs[[x,x^2,1+x^3],[y,y^2,1+y^3],[z,z^2,1+z^3]] , Where x,y,z are different. Show that if Delta=0 ,then 1+xyz=0

Without expanding the determinant prove the following. |[b+c,q+r,y+z],[c+a,r+p,z+x],[a+b,p+q,x+y]|=2|[a,p,x],[b,q,y],[c,r,z]|

MAXIMUM PUBLICATION-MODEL QUESTION-EXAMPLE
  1. Find x and y if x[[2],[3]]+y[[-1],[1]]=[[10],[5]]

    Text Solution

    |

  2. Express the matrix [[2,-2,-4],[-1,3,4],[1,-2,-3]] as the sum of a ...

    Text Solution

    |

  3. prove that abs[[a,b,c],[a+2x,b+2y,c+2z],[x,y,z]]=0

    Text Solution

    |

  4. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] Prov...

    Text Solution

    |

  5. if A=[[1,-1,2],[0,2,-3],[3,-2,4]] B=[[-2,0,1],[9,2,-3],[6,1,-2]] ...

    Text Solution

    |

  6. Prove that the function defined by f(x)= cosx^2 is a continuous f...

    Text Solution

    |

  7. if y=e^(a cos^-1x),-1lexle1, show that dy/dx= (-ae^(acos^-1x))/(...

    Text Solution

    |

  8. Evaluate int sin mxdx

    Text Solution

    |

  9. Evaluate int 1/(sqrt (x^2+2x+2))dx

    Text Solution

    |

  10. Evaluate int x/((x+1)(x+2))dx

    Text Solution

    |

  11. if bara=3i+2j+2k,barb=i+2j-2k find bara+barb,bara-barb

    Text Solution

    |

  12. if bara=3i+2j+2k,barb=i+2j-2k find a unit vector perpendicular to bo...

    Text Solution

    |

  13. Consider the points A(1.2.7),B(2,6,3),C(3,10,-1) find bar(AB),bar(BC...

    Text Solution

    |

  14. Consider the points A(1,2,7),B(2,6,3),C(3,10,-1) prove that A,B,C ar...

    Text Solution

    |

  15. Find the angles between the lines (x-2)/2=(y-1)/5=(z+3)/-3 and (x+...

    Text Solution

    |

  16. find the shortest distance between the pair of lines barr=(i+2j+3k)...

    Text Solution

    |

  17. The probability distribution of a random variable is given by p(x) . W...

    Text Solution

    |

  18. The following is a probability distribution function of a random vari...

    Text Solution

    |

  19. Construct a 2times2 matrix whose elements are given a(ij)=2i+j

    Text Solution

    |

  20. Construct a 2times2 matrix whose elements are given a(ij)=2i+j.find A^...

    Text Solution

    |