Home
Class 12
MATHS
Show that the matrix A=[{:(2,3),(1,2):}]...

Show that the matrix `A=[{:(2,3),(1,2):}]` satisfies the equation `A^2-4A+I=O`, where I is `2xx2` identity matrix and O is `2xx2` zero matrix. Using this equation find `A^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
`A^(-1)=[{:(2,-3),(-1,2):}]`
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Short Answer Type Questions)|17 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|6 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|42 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 5 (Section-D)|4 Videos

  • INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER-7 (SECTION-D)|2 Videos

Similar Questions

Explore conceptually related problems

Show that A=[{:(5,3),(-1,-2):}] satisfies the equation A^(2)=3A-7I=0 and hence find A^(-1) .

For the matrix A=[{:(2,3),(1,2):}] , show that A^2-4A+I_2=0 . Hence, find A^(-1)

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.

A=[{:(4,3),(2,5):}],A^(2)-xA+yI=0 . Find real numbers x and y. where I is a 2xx2 identity matrix.

For the matrix A=[{:(3,2),(1,1):}] , find the numbers a and b such that A^2+aA+bI=O

If A=[{:(3,1),(-1,2):}] , show that A^(2)-5A+7I=O .

For the matrix A=[{:(1,2,2),(2,1,2),(2,2,1):}] . Show that A^2-4A-5I=0 Hence find A^(-1)

The matrix A=[{:(1,0,0),(0,2,0),(0,0,4):}] is a .......

If A=[{:(1,2,3),(3,-2,1),(4,2,1):}] , then show that A^(3)-23A-40I=O .

Let A A=[{:(0,1),(0,0):}] , show that (aI+bA)^(n)=a^(n)I+na^(n-1)bA , where I is the identity matrix of order 2 and n in N .

KUMAR PRAKASHAN-DETERMINANTS -Textbook Illustrations for Practice work
  1. If x,y,z are different and Delta=|{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z,z...

    Text Solution

    |

  2. Prove that |{:(a+1,1,1),(1,b+1,1),(1,1,c+1):}|=abc(1/a+1/b+1/c+1)

    Text Solution

    |

  3. Find the area of the triangle whose vertices are (3,8),(-4,2) and (5,1...

    Text Solution

    |

  4. Find the equation of the line joining A(1,3) and B(0,0) using determin...

    Text Solution

    |

  5. Find the minor of elements 6 in the determinant Delta=|{:(1,2,3),(4,...

    Text Solution

    |

  6. Find minors and cofactors of all the elements of the determinant |{:(1...

    Text Solution

    |

  7. Find minors and cofactors of the elements a(11),a(21) in the determina...

    Text Solution

    |

  8. Find minors and cofactors of the elements of the determinant |{:(2,-3,...

    Text Solution

    |

  9. Find adj A for A = {:[( 2,3),( 1,4) ]:}

    Text Solution

    |

  10. If A=[{:(1,3,3),(1,4,3),(1,3,4):}] , then verify that A adjA=|A|I. Als...

    Text Solution

    |

  11. If A=[{:(2,3),(1,-4):}] and B=[{:(1,-2),(-1,3):}] then verify that (AB...

    Text Solution

    |

  12. Show that the matrix A=[{:(2,3),(1,2):}] satisfies the equation A^2-4A...

    Text Solution

    |

  13. Solve the system of equations {:(2x+5y=1),(3x+2y=7):},

    Text Solution

    |

  14. Solve system of linear equations , using matrix method if exists 4x-...

    Text Solution

    |

  15. The sum of three numbrs is 6. If we multiply third number by 3 and add...

    Text Solution

    |

  16. If a,b,c are positive and unequal, show that value of the determinant ...

    Text Solution

    |

  17. If a,b,c are in A.P find value of |{:(2y+4,5y+7,8y+a),(3y+5,6y+8,9y+...

    Text Solution

    |

  18. show that [((x+y)^2 , zx , zy),( zx, (z+y)^2 ,xy),(zy,xy,(z+x)^2)]=2...

    Text Solution

    |

  19. Solve following system using matrix x-y+2z =1 , 2y -3z =1, 3x...

    Text Solution

    |

  20. Prove that |{:(a+bx,c+dx,p+qx),(ax+b,cx+d,px+q),(mu,vartheta,omega):}|...

    Text Solution

    |