1.

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

Answer» `"Let A ="|{:(1,-1,2),(0,2,-3),(3,-2,4):}|`
`rArr" |A|="|{:(1,-1,2),(0,2,-3),(3,-2,4):}|`
=1(8-6)-(-1)(0+9)+2(0-6)
=2+9-12=-1
`A_(11)=(-1)^(2)(8-6)=2,A_(12)=(-1)^(3)(0+9)=-9`
`A_(13)=(-1)^(4)(0-6)=-6`
`A_(21)=(-1)^(3)(-4+4)=0,A_(22)=(-1)^(4)(4-6)=-2`
`A_(23)=(-1)^(5)(-2+3)=-1`
`A_(31)=(-1)^(4)(3-4)=-1,A_(32)=(-1)^(5)(-3-0)=3`
`A_(33)=(-1)^(6)(2-0)=2`
`therefore" adj A"=|{:(2,-9,-6),(0,-2,-1),(-1,3,2):}|=|{:(2,0,-1),(-9,-2,3),(-6,-1,2):}|`
`"Now A"^(1)=1/|A|".adj A "=1/-1|{:(2,0,-1),(-9,-2,3),(-6,-1,2):}|`
`|{:(-2,0,1),(9,2,-3),(6,1,-2):}|`


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