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If A = [(1,0,2),(0,2,1),(2,0,3)], prove ...

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

Answer

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If A = [{:(1,0,2),(0,2,1),(2,0,3):}],Provethat A^(3)-6A^(2)+7A+21=0

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) .

Knowledge Check

  • If A = [(1,2,1),(0,1,-1),(3,-1,1)] , then A^(3) - 3A^(2) - A +9I equals :

    A
    I
    B
    O
    C
    A
    D
    `A^(2)`

  • If [(2,1,0),(0,2,1),(1,0,2)] then |adjA|=

    A
    43839
    B
    81
    C
    0
    D
    9

  • If A = [ (3,2),(0,1] , then A^(-3) is :

    A
    `1/27 [(1,-26),(0,27)] `
    B
    `1/27 [(-1,26),(0,-27)] `
    C
    `1/27 [(1,-26),(0,-27)] `
    D
    `1/27 [(-1,-26),(0,-27)] `

    • Similar Questions

    Explore conceptually related problems

    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 = [(2,0,1),(0,-3,0),(0,0,4)] , verify A^(3) - 3A^(2) - 10A + 24I = 0 where 0 is zero matrix of order 3 xx 3 .

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

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

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

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