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

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

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(7) {:[(2,-1),(1,3)]:}`
Promotional Banner

Similar Questions

Explore conceptually related problems

If A=[(3,1),(-1,2)] , show that A^(2)-5A+7I=0 .

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

Solve the following equations by matrix method. For the matrix A = [(1,1,1),(1,2,-3),(2,-1,3)] . Show that A^(3) - 6A^(2) + 5A + 11 I = 0 . Hence, find A^(-1) .

If A=[(k,l),(m,n)] and kn!=lm, show that A^(2)-(k+n)A+(kn-lm)I=0. Hence, find A^(-1)

If A=[(1,2,3),(3,-2,1),(4,2,1)] then show that A^3-23A -40 I=0 .

Solve the following equations by matrix method. If A = [(2,-1,1),(-1,2,-1),(1,-1,2)] verify that A^(3) - 6A^(2) + 9A = 4 I = 0 and hence, find A^(-1) .

If A=[{:(,1,2,3),(,3,-2,1),(,4,2,1):}] then show that A^(3)-23A-40I=0

For the matrix A=[[3, 2],[ 1, 1]] , find the numbers a and b such that A^2+a A+b I=O . Hence, find A^(-1) .

If A =[{:(1,2,3),(3,-2,1),(4,2,1):}] then show that A^(3)-23A - 40 I =0

If A = [(7,3),(5,2)] find A^(-1) .