Home
Class 12
MATHS
If A=[{:(1,0,2),(0,2,1),(2,0,3):}] then...

If `A=[{:(1,0,2),(0,2,1),(2,0,3):}]` then , prove that
`A^(3)-6A^(2)+7A+2I=O`.

Text Solution

Verified by Experts

The correct Answer is:
`[{:(0,0,0),(0,0,0),(0,0,0):}]=O=R.H.S`.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    KUMAR PRAKASHAN|Exercise EXERCISE -3.3|11 Videos

  • MATRICES

    KUMAR PRAKASHAN|Exercise EXERCISE -3.4|18 Videos

  • MATRICES

    KUMAR PRAKASHAN|Exercise Practice Paper - 3 (Section - D)|1 Videos

  • LINEAR PROGRAMMING

    KUMAR PRAKASHAN|Exercise PRACTICE WORK|25 Videos

  • PROBABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 13 (Section - D (Answer the following questions))|2 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(1,2,1),(2,1,3),(1,1,0):}] then prove that A^3-2A^2-7A-4I_3=0 . Hence find A^(-1)

For matrix A=[{:(1,1,1),(1,2,-3),(2,-1,3):}] . Prove that , A^(3)-6A^(2)+5A+11I=0 . Hence find A^(-1) using it .

If A=[{:(1,0,-1),(2,1,3),(0,1,1):}] , then verify that A^(2)+A=A(A+I) where I is 3xx3 unit matrix.

If A=[{:(0,1),(0,0):}]andI=[{:(1,0),(0,1):}] then prove that (aI+bA)^(3)=a^(3)I+3a^(2)bA .

For the matrix A=[{:(1,1,1),(1,2,-3),(2,-1,3):}] Show that A^3-6A^2+5A+11I=O . Hence find A^(-1)

If A=[{:(2,-1,1),(-1,2,-1),(1,-1,2):}] Verify the result A^3-6A^2+9A-4I=O and hence find A^(-1)

If A=[{:(3,-2),(4,-2):}]andI=[{:(1,0),(0,1):}] , find k so that A^(2)=kA-2I .

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

If A=[{:(-1,2,3),(5,7,9),(-2,1,1):}]andB=[{:(-4,1,-5),(1,2,0),(1,3,1):}] , then verify that (i) (A+B)'=A'+B' (ii) (A-B)'=A'-B'.

KUMAR PRAKASHAN-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):}]a...

    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,sintheta),(-sintheta,costheta):}]+s...

    Text Solution

    |

  5. Find X and Y,if X+Y=[{:(5,2),(0,9):}]andX-Y=[{:(3,6),(0,-1):}].

    Text Solution

    |

  6. Find X , if Y=[{:(3,2),(1,4):}]and2X+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...

    Text Solution

    |

  9. If x[{:(2),(3):}]+y[{:(-1),(1):}]=[{:(10),(5):}], find thevalues of x ...

    Text Solution

    |

  10. Given 3[{:(x,y),(z,w):}]=[{:(x,6),(-1,2w):}]+[{:(4,x+y),(z+w,3):}], fi...

    Text Solution

    |

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

    Text Solution

    |

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

    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):}] then , prove that A^(3)-6A^(2)+7...

    Text Solution

    |

  15. If A=[{:(3,-2),(4,-2):}]andI=[{:(1,0),(0,1):}], find k so that A^(2)=...

    Text Solution

    |

  16. If A=[{:(0,"tan"(alpha)/(2)),("tan"(alpha)/(2),0):}]and I theidentity ...

    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 d...

    Text Solution

    |

  19. Assume X, Y, Z, W and P Are Matrices of Order 2 x n, 3 x k, 2 x p, n x...

    Text Solution

    |

  20. Assume X, Y, Z, W and P Are Matrices of Order 2 x n, 3 x k, 2 x p,N x ...

    Text Solution

    |