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[{:(-1,1,2),(1,2,3),(3,1,1):}]...

`[{:(-1,1,2),(1,2,3),(3,1,1):}]`

Answer

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Obtain the inverse of the following matrix using elementary operations A=[(0,1,2),(1,2,3),(3,1,1)]

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

Knowledge Check

  • If [ 1 " "x " "0] {:[(1,1,1),(2,2,2),(3,3,3)]:}{:[(1),(1),(x)]:}=0 then x=

    A
    2 or 14
    B
    `-2` or `x=-1//2`
    C
    2 or 16
    D
    `-2` or `16`.

  • Let A = [(1,-1,1),(2,1,-3),(1,1,1)] and (10)B = [(4,2,2),(-5,0,alpha),(1,-2,3)] If B is the inverse of A , then alpha is :

    A
    `-2`
    B
    `-1`
    C
    2
    D
    5

  • 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)`

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

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

    If {:A=[(0,1,-1),(2,1,3),(3,2,1)]:} then (A(adj A)A^(-1))A=

    Use the product [(1,-1,2),(0,2,-3),(3,-2,4)][(-2,-0,1),(9,2,-3),(6,1,-2)] to solve the system of equations x - y + 2z = 1 2y - 3z = 1 3x - 2y + 4z = 2

    If A=[(1,1,-1),(2,0,3),(3,-1,2)],B=[(1,3),(0,2),(-1,4)] and C=[(1,2,3,-4),(2,0,-2,1)] , find A(BC), (AB)C and show that (AB)C=A(BC) .

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