Home
Class 12
MATHS
Consider the matrix A=[[a,b,c],[b,c,a],[...

Consider the matrix `A=[[a,b,c],[b,c,a],[c,a,b]]`
show that `abs[A]=-(a^3+b^3+c^3-3abc)`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY & DIFFERENTIABILITY

    MAXIMUM PUBLICATION|Exercise EXAMPLE|178 Videos

  • DIFFERENTIAL EQUATION

    MAXIMUM PUBLICATION|Exercise EXAMPLE|81 Videos

Similar Questions

Explore conceptually related problems

Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] Find Axxadj(A) if a=1 , b=10 , c=100

Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] Using the column operation C_1rarrC_1+C_2+C_3 , show that abs[A]=(a+b+c)abs[[1,b,c],[1,c,a],[1,a,b]]

Show that abs [[1,a,bc],[1,b,ac],[1,c,ab]]=(a-b)(b-c)(c-a)

Show that abs[[a+b,b+c,c+a],[b+c,c+a,a+b],[c+a,a+b,b+c]]=2abs[[a,b,c],[b,c,a],[c,a,b]]

Prove that abs[[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=(a+b+c)^3

Consider abs[[a,a+b,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b,10a+6b+3c]]

Consider the matrices A=[[1,-2],[-1,3]] and B=[[a,b],[c,d]] If AB=[[2,9],[5,6]] , find the values of a,b,c,d

If a,b,c are real numbers and abs[[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]]=0 ,show that a=b=c

Using properties of determinants, show that abs[[a,a^2,b+c],[b,b^2,c+a],[c,c^2,a+b]]=(b-c)(c-a)(a-b)(a+b+c)

If a, b, c are positive and unequal show that value of the determinant Delta=|[a, b, c],[ b, c, a],[ c, a, b]| is negative.

MAXIMUM PUBLICATION-DETERMINANTS-EXAMPLE
  1. Consider the matrix A=[[2,5],[3,2]] Using A^-1 solve the system of l...

    Text Solution

    |

  2. Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] Using the column ope...

    Text Solution

    |

  3. Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] show that abs[A]=-(a...

    Text Solution

    |

  4. Consider the matrix A=[[a,b,c],[b,c,a],[c,a,b]] Find Axxadj(A) if a=...

    Text Solution

    |

  5. If A=[[1,1,5],[0,1,3],[0,-1,-2]] what is the value of abs[3A]?

    Text Solution

    |

  6. Find the equation of the line joining the points(1,2) and (-3,-2) us...

    Text Solution

    |

  7. Show that abs[[1,a,a^2],[1,b,b^2],[1,c,c^2]]=(a-b)(b-c)(c-a)

    Text Solution

    |

  8. Consider the following system of linear equations, x+y+z=6,x-y+z=2, ...

    Text Solution

    |

  9. Consider the following system of linear equations, x+y+z=6,x-y+z=2, ...

    Text Solution

    |

  10. Consider the following system of linear equations, x+y+z=6,x-y+z=2, ...

    Text Solution

    |

  11. If abs[[x,3],[5,2]]=5,then x=…..

    Text Solution

    |

  12. Prove that abs[[y+k,y,y],[y,y+k,y],[y,y,y+k]]=k^2(3y+k)

    Text Solution

    |

  13. Solve the following system of linear Equations,using matrix method, ...

    Text Solution

    |

  14. Let B is a square matrix of order 5, then abs[kB] is equal to….

    Text Solution

    |

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

    Text Solution

    |

  16. Check the consistency of the following equations, 2x+3y+z=6,x+2y-z...

    Text Solution

    |

  17. Find the values of x in which abs[[3,x],[x,1]]=abs[[3,2],[4,1]]

    Text Solution

    |

  18. Using the property of determinants,show that the points A(a,b+c),B(b...

    Text Solution

    |

  19. Examine the consistency of system of following equations: 5x-6y+4z...

    Text Solution

    |

  20. Consider a system of linear equations which is given below, 2/x+3/y+10...

    Text Solution

    |