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(ii) 
Asked by Kalyani Last Modified
Answer (i) The given determinant is.
By the definition of minors and cofactors, we have:
M11 = minor of a11= 
M12 = minor of a12= 
M13 = minor of a13 = 
M21 = minor of a21 =
M22 = minor of a22 =
M23 = minor of a23 = 
M31 = minor of a31= 
M32 = minor of a32 =
M33 = minor of a33 =
A11 = cofactor of a11= (−1)1+1 M11 = 1
A12 = cofactor of a12 = (−1)1+2 M12 = 0
A13 = cofactor of a13 = (−1)1+3 M13 = 0
A21 = cofactor of a21 = (−1)2+1 M21 = 0
A22 = cofactor of a22 = (−1)2+2 M22 = 1
A23 = cofactor of a23 = (−1)2+3 M23 = 0
A31 = cofactor of a31 = (−1)3+1 M31 = 0
A32 = cofactor of a32 = (−1)3+2 M32 = 0
A33 = cofactor of a33 = (−1)3+3 M33 = 1
(ii) The given determinant is.
By definition of minors and cofactors, we have:
M11 = minor of a11= 
M12 = minor of a12= 
M13 = minor of a13 = 
M21 = minor of a21 = 
M22 = minor of a22 = 
M23 = minor of a23 = 
M31 = minor of a31= 
M32 = minor of a32 = 
M33 = minor of a33 = 
A11 = cofactor of a11= (−1)1+1 M11 = 11
A12 = cofactor of a12 = (−1)1+2 M12 = −6
A13 = cofactor of a13 = (−1)1+3 M13 = 3
A21 = cofactor of a21 = (−1)2+1 M21 = 4
A22 = cofactor of a22 = (−1)2+2 M22 = 2
A23 = cofactor of a23 = (−1)2+3 M23 = −1
A31 = cofactor of a31 = (−1)3+1 M31 = −20
A32 = cofactor of a32 = (−1)3+2 M32 = 13
A33 = cofactor of a33 = (−1)3+3 M33 = 5
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