Find the inverse the matrix (if it exists)given in `[1 0 0 3 3 0 5 2-1]`

Monjur Alahi

Find the inverse the matrix (if it exists)given in `[1 0 0 3 3 0 5 2-1]`


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Salim Ahmed Kawsar

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`"Let a ="|{:(1,0,0),(3,3,0),(5,2,-1):}|`
`rArr" "|A|=|{:(1,0,0),(3,3,0),(5,2,-1):}|=1(-3-0)-0+0`
`=-3ne0`
`therefore A^(-1)"exists"`.
`A_(11)=(-1)^(2)(-3-0)=-3,A_(12)=(-1)^(3)(-3-0)=3`,
`A_(13)=(-1)^(4)(6-15)=-9`
`A_(21)=(-1)^(3)(0-0)=0,A_(22)=(-1)^(4)(-1-0)=-1`,
`A_(23)=(-1)^(5)(2-0)=-2`,
` A_(31)=(-1)^(4)(0-0)=0,A_(32)=(-1)^(5)(0-0)=0,`
`A_(33)=(-1)^(6)(3-0)=3`
`therefore" adj A ="|{:(-3,3,-9),(0,-1,-2),(0,0,3):}|=|{:(-3,0,0),(3,-1,0),(-9,-2,3):}|`
`"Now A"^(-1)=1/|A|"adj A ="1/-3|{:(-3,3,-9),(0,-1,-2),(0,0,3):}|`

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