Let Mij and Cij represents the minor and co–factor of an element, where i and j represent the row and column. The minor of the matrix can be obtained for a particular element by removing the row and column where the element is present. Then finding the absolute value of the matrix newly formed.
Also, Cij = (–1)i+j × Mij
\( M_{11}=ab^2-ac^2\)
\( M_{21}=a^2b-c^2b\)
M31 = a × c a – b × bc
M31 = a2c – b2c
C11 = (–1)1+1 × M11
= 1 × (ab2 – ac2)
= ab2 – ac2
C21 = (–1)2+1 × M21
= –1 × (a2b – c2b)
= c2b – a2b
C31 = (–1)3+1 × M31
= 1 × (a2c – b2c)
= a2c – b2c
Now expanding along the first column we get
|A| = a11 × C11 + a21× C21+ a31× C31
= 1× (ab2 – ac2) + 1 × (c2b – a2b) + 1× (a2c – b2c)
= ab2 – ac2 + c2b – a2b + a2c – b2c
Answered by Sakshi | 1 year agoEvaluate
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