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Find minor and cofactors or all the elem...

Find minor and cofactors or all the elements of determinant `|{:(-1,2,3),(-4,5,-2),(6,4,8):}|`

Text Solution

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`Delta=|{:(-1,2,3),(-4,5,-2),(6,4,8):}|`
`M_11="Minor of "a_11(-1)=|{:(5,-2),(4,8):}|=48`
`M_12="Minor of "a_12(-2)=|{:(-4,-2),(6,8):}|=-20`
`M_13="Minor of "a_13(-3)=|{:(-4,5),(6,4):}|=-46`
`M_21="Minor of "a_21(-4)=|{:(2,3),(4,8):}|=4`
`M_22="Minor of "a_22(5)=|{:(-1,3),(6,8):}|=-26`
`M_23="Minor of "a_23(-2)=|{:(-1,2),(6,4):}|=-16`
`M_34="Minor of "a_31(6)=|{:(2,3),(5.-2):}|=-19`
`M_32="Minor of "a_32(4)=|{:(-1,3),(-4,-2):}|=14`
`M_33="Minor of "a_33(8)=|{:(-1,2),(-4,5):}|=3`
Cofactors
`A_11=(-1)^(1+1)M_11=48`
`A_12(-1)^(1+2)M_12=20`
`A_(13)=(-1)^(1+3)M_(13)=-46`
`A_(21)=(-1)^(2+1)M_(21)=-4`
`A_(22)=(-1)^(2+2)M_(22)=-26`
`A_(23)=(-1)^(2+3)M_(32)=16`
`A_(31)=(-1)^(3+1)M_(31)=-19`
`A_(32)=(-1)^(3+2)M_(32)=-14`
`A_(33)=(-1)^(3+3)M_(33)=3`
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