Math Assignment Help With Introduction To Determinants
3.6 Introduction to Determinants:
The value of determinant of a(1x1) matrix [a] is defined as |a| = 1
Value of determinant of order 2 is defined as
Value of determinant of order 3 or more is determined by finding minor of aij in |a| and co-factor in aij in |a|.
Minor of aij in |a| is defined as the value of the determinant obtained by deleting the ith row and jth column of |A| and is denoted by Mij.
Co-factor of aij in |A| is defined as
Similarly, we can obtain the minor of each one of the remaining elements.
Now if we denote the co-factor of aij by cij, then,
C11 = (-1)1+1. M11 = (a22a33 – a32a23);
C12 = (-1)1+2. M12 = -M12 = (a31a23 – a21a33)
C13 = (-1)1+3. M13 = M13 = (a21a32 – a31a22)
C21 = (-1)2+1. M21 = - M21 = (a32a13 – a12a33)
Similarly, the co-factor of each one of the remaining elements of ∆ can be obtained.
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