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Find the adjoint of each of the matrices...

Find the adjoint of each of the matrices `[{:(1,2),(3,4):}]`

Text Solution

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`Let A=[{:(1,2),(3,4):}]`
`A_(11)=(-1)^(1+1),4=4`
`A_(12)=(-1)^(1+2).3=-3,`
`A_(21)=(-1)^(2+1).2=-2,`
`A_(22)=(-1)^(2+2).1=1`
`therefore" adj A ="[{:(A_(11),A_(12)),(A_(21),A_(22)):}]`
`[{:(4,-3),(-2,1):}]=[{:(4,-2),(-3,1):}]`
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Knowledge Check

  • The adjoint of the matrix A= [{:( 1,2),( 3,-5) :}] is

    A
    `[{:( -5,-2),( -3,1):}]`
    B
    ` [{:( 5,2),( 3,-1) :}]`
    C
    ` [{:( 5,-2),( 3,-1) :}]`
    D
    ` [{:( 5,-2),( -3,-1):}]`

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