Q. 2 A3.9( 10 Votes )

Write Minors and

Answer :

Minor of an element aij = Mij

a11 = 1, Minor of element a11 = M11 = = (1 × 1) – (0 × 0) = 1


Here removing 1st row and 1st column from the determinant we are left out with the determinant. Solving this we get M11 = 1


Similarly, finding other Minors of the determinant


a12 = 0, Minor of element a12 = M12 = = (0 × 1) – (0 × 0) = 0


a13 = 0, Minor of element a13 = M13 = = (0 × 0) - (1 × 0) = 0


a21 = 0, Minor of element a21 = M21 = = (0 × 1) – (0 × 0) = 0


a22 = 1, Minor of element a22 = M22 = = (1 × 1) – (0 × 0) = 1


a23 = 0, Minor of element a23 = M23 = = (1 × 0) – (0 × 0) = 0


a31 = 0, Minor of element a31 = M31 = = (0 × 0) – (0 × 1) = 0


a32 = 0, Minor of element a32 = M32 = = (1 × 0) – (0 × 0) = 0


a33 = 1, Minor of element a33 = M33 = = (1 × 1) – (0 × 0) = 1


Cofactor of an element aij, Aij = (-1)i+j × Mij


A11 = (-1)1+1 × M11 = 1 × 1 = 1


A12 = (-1)1+2 × M12 = (-1) × 0 = 0


A13 = (-1)1+3 × M13 = 1 × 0 = 0


A21 = (-1)2+1 × M21 = (-1) × 0 = 0


A22 = (-1)2+2 × M22 = 1 × 1 = 1


A23 = (-1)2+3 × M23 = (-1) × 0 = 0


A31 = (-1)3+1 × M31 = 1 × 0 = 0


A32 = (-1)3+2 × M32 = (-1) × 0 = 0


A33 = (-1)3+3 × M33 = 1 × 1 = 1


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