Home
Class 12
MATHS
Find A^(2)-5A=6I, if A=[(2,0,1),(2,1,3),...

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

Text Solution

Verified by Experts

The correct Answer is:
`[(1,-1,-3),(-1,-1,-10),(-5,4,4)]`
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

Let A+2B=[(1,2,0),(6,-1,3),(-5,3,1)] and 2A-B=[(2,-1,5),(2,-1,6),(0,1,2)], then find tr(A)-tr(B).

Find the matrix A if [(1,2),(0,1)]A=[(6,1),(2,1)]

Show that (i) [(5,-1),(6,7)][(2,1),(3,4)] ne [(2,1),(3,4)][(5,-1),(6,7)] (ii) [(1,2,3),(0,1,0),(1,1,0)][(-1,1,0),(0,-1,1),(2,3,4)] ne [(-1,1,0),(0,-1,1),(2,3,4)][(1,2,3),(0,1,0),(1,1,0)]

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) .

Find x, if [(x, -5, -1)][(1,0,2),(0,2,1),(2,0,3)][(x),(4),(1)]=O

Using elementary transformations, find the inverse of the matrices [(2,0,-1),(5,1,0),(0,1,3)]

If A= [(1,0),(3,-1),(2,4)] and B= [(3,1,-2),(4,6,0)] find BA

Find the rank of the following matrices by minor method: (i) [{:(2,-4),(-1,2):}] (ii) [{:(-1,3),(4,-7),(3,-4):}] (iii) [{:(1,-2,-1,0),(4,-6,-3,1):}] (iv) [{:(1,-2,3),(2,4,-6),(5,1,-1):}] (v) [{:(0,1,2,1),(0,2,4,3),(8,1,0,2):}]

Find the rank of the following matrices. [{:(0,1,2,1),(2,-3,0,-1),(1,1,-1,0):}]

Let a be a 3xx3 matric such that [(1,2,3),(0,2,3),(0,1,1)]=[(0,0,1),(1,0,0),(0,1,0)] , then find A^(-1) .

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

    |