Home
Class 12
MATHS
If A=[(1,0,2),(0,2,1),(2,0,3)], prove th...

If `A=[(1,0,2),(0,2,1),(2,0,3)]`, prove that `A^(3)-6A^(2)+7A+2I=0`

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    NCERT TAMIL|Exercise EXERCISE 3.3|12 Videos

  • MATRICES

    NCERT TAMIL|Exercise EXERCISE 3.4|18 Videos

  • MATRICES

    NCERT TAMIL|Exercise EXERCISE 3.1|10 Videos

  • LINEAR PROGRAMMING

    NCERT TAMIL|Exercise MISCELLANEOUS EXERCISE|5 Videos

  • ORDINARY DIFFERENTIAL EQUATIONS

    NCERT TAMIL|Exercise EXERCISE 10.9|25 Videos

Similar Questions

Explore conceptually related problems

If A = [(1,0,2),(0,2,1),(2,0,3)] "and" " "A^(3)-6A^(2)+7A+kI=0, find the value of k.

If A=[{:(2,-1,1),(-1,2,-1),(1,-1,2):}] verify that A^(3)-6A^(2)+9A-4I=0 and hence find A^(-1) .

If A=[(0,1,1),(1,0,1),(1,1,0)] show that A^(-1)=1/2(A^(2)-3I) .

If A= [(2,1,2),(4,2,-3),(0,5,1)] ,B= [(-2,1,0),(2,1,-1),(1,0,1)] .Prove that (AB)^(T)=B^(T)A^(T)

If A= [(2,3,1),(1,0,2),(2,1,0)] compute A^(2) .

If A= [{:(0,1,1),(1,0,1),(1,1,0):}], "show that" A^(-1)=(1)/(2)(A^(2)-3I)

If A=[{:(0,1,1),(1,0,1),(1,1,0):}] show that A^(-1)=(1)/(2)(A^(2)=3I)

Given A=[{:(1,-1,2),(3,0,-2),(1,0,3):}] verify that A(adjA)_=(adjA)A=|A|I_(3) .

NCERT TAMIL-MATRICES-EXERCISE 3.2
  1. Compute the indicated products: (i) [(a,b),(-b,a)][(a,-b),(b,a)] (i...

    Text Solution

    |

  2. If A=[(1,2,-3),(5,0,2),(1,-1,1)],B=[(3,-1,2),(4,2,5),(2,0,3)] and C=[(...

    Text Solution

    |

  3. If A=[((2)/(3), 1,(5)/(3)),((1)/(3), (2)/(3), (4)/(3)),((7)/(3), 2, (2...

    Text Solution

    |

  4. Simplify costheta[(costheta,sin theta),(-sintheta,costheta)]+sin[(sint...

    Text Solution

    |

  5. Find X and Y, if (i) X+Y=[(7,0),(2,5)] and X-Y=[(3,0),(0,3)] (ii) ...

    Text Solution

    |

  6. Find X, if Y=[(3,2),(1,4)] and 2X+Y=[(1,0),(-3,2)]

    Text Solution

    |

  7. Find x and y, if 2[(1,3),(0,x)]+[(y,0),(1,2)]=[(5,6),(1,8)]

    Text Solution

    |

  8. Solve the equation for x, y, z and t, if 2[(x, z),(y,t)]+3[(1,-1),(0,2...

    Text Solution

    |

  9. If x[(2),(3)]+y[(-1),(1)]=[(10),(5)], find the value of x and y.

    Text Solution

    |

  10. Given 3[(x,y),(z,w)]=[(x,6),(-1,2w)]+[(4,x+y),(z+w,3)], find the value...

    Text Solution

    |

  11. If F(x)=[(cosx,-sinx,0),(sinx,cosx,0),(0,0,1)], show that F(x) F(y)=F(...

    Text Solution

    |

  12. Show that (i) [(5,-1),(6,7)][(2,1),(3,4)] ne [(2,1),(3,4)][(5,-1),(6...

    Text Solution

    |

  13. Find A^(2)-5A=6I, if A=[(2,0,1),(2,1,3),(1,-1,0)]

    Text Solution

    |

  14. If A=[(1,0,2),(0,2,1),(2,0,3)], prove that A^(3)-6A^(2)+7A+2I=0

    Text Solution

    |

  15. If A=[(3,-2),(4,-2)] and I=[(1,0),(0,1)], find k so that A^(2)=kA-2I

    Text Solution

    |

  16. If A=[(0,-"tan"(alpha)/(2)),("tan"(alpha)/(2),0)] and I is the identit...

    Text Solution

    |

  17. A trust fund has Rs. 30,000 that must be invested in two different typ...

    Text Solution

    |

  18. The bookshop of a particular school has 10 dozen chemistry books, 8 do...

    Text Solution

    |

  19. Assume X, Y, Z, W and P are matrices of order 2xx n, 3xxk, 2xxp, n xx...

    Text Solution

    |

  20. Assume X, Y, Z, W and P are matrices of order 2xx n, 3xxk, 2xxp, n xx...

    Text Solution

    |