Home
Class 12
MATHS
Show that the matrix A=({:(2,-3),(3,4):}...

Show that the matrix `A=({:(2,-3),(3,4):})` satisfies the equation `A^(2)-6A+17I=O` and hence find `A^(-1)` where I is the identity matrix and O is the null matrix of order `2 times 2`.

Text Solution

Verified by Experts

The correct Answer is:
`A^(-1)=1/17({:(4,3),(-3,2):})`
Promotional Banner

Topper's Solved these Questions

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise WBHS ARCHIVE 2015|7 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise WBHS ARCHIVE 2016|7 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise WBHS ARCHIVE 2013|5 Videos

  • ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

  • ARCHIVE

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|13 Videos

Similar Questions

Explore conceptually related problems

Show that the matrix A= [(2,-3),(3,4)] satisfies the equation x^(2) - 6x + 17 = 0. Hence find A^(-1)

Show that the matrix A=[[1,2,2],[2,1,2],[2,2,1]] satisfies the equation A^2-4A-5I_3=O and hence find A^(-1)

Show that, the matrix A = [(1,2,2),(2,1,2),(2,2,1)] satisfies the equation A^(2) - 4A - 5I_(3) = 0 and hence find A^(-1) .

If the matrix A = [(1,2),(3,4)] satisfies the equation A^(2) = 5A + 2I . Then, find the value of A^-1 .

Show that the matrix A = {:[( 2,3),( 1,2) ]:} satisfies equation A^(2) -4A +I=0 where is 2xx2 identity matrix and O is 2xx2 Zero matrix. Using this equation, Find A^(-1)

If matrix A satisfies the equation A^2+5A+6I=0 then A^3 is

If A=({:(5,8),(8,13):}) , show that the matrix equation x^(2)-18x+1=0 is satisfied by both the matrices A and A^(_1) (I is the identity matrix of order two).

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

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

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