1.

Find the inverse the matrix (if it exists) given in`[[2, 1, 3],[ 4,-1, 0],[-7, 2, 1]]`

Answer» `"Let A ="|{:(2,1,3),(4,-1,0),(-7,2,1):}|`
`rArr" "|A|=|{:(2,1,3),(4,-1,0),(-7,2,1):}|`
`=2,(-1-0)-1(4-0)+3(8-7)`
`=-2-4+3=-3ne0`
`A_(11)=(-1)^(2)(-1-0)=-1`
`A_(12)=(-1)^(3)(4-0)=-4`,
`A_(13)=(-1)^(4)(8-7)=1,`
`A_(21)=(-1)^(3)(1-6)=5`,
`A_(22)=(-1)^(4)(2+21)=23`
`A_(23)=(-1)^(5)(4+7)=-11,`
`A_(31)=(-1)^(4)(0+3)=3`
`A_(32)=(-1)^(4)(0+3)=3`
`A_(33)=(-1)^(6)(-2-4)=-6`
`therefore" adj A"=|{:(-1,-4,1),(5,23,-11),(3,12,-6):}|=|{:(-1,5,3),(-4,23,12),(1,-11,-6):}|`
`"Now A"^(-1)=1/|A|"adj A"=-1/3|{:(-1,5,3),(-4,23,12),(1,-11,-6):}|`


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