Using Cofactors of elements of second row, evaluate △=\(\begin{vmatrix}5&3&8\\2&0&1\\1&2&3\end{vmatrix}\)
The given determinant is \(\begin{vmatrix}5&3&8\\2&0&1\\1&2&3\end{vmatrix}\)
We have:
M21=\(\begin{vmatrix}3&8\\2&3\end{vmatrix}\)=9-16=-7
∴A21=cofactor of a21=(−1)2+1 M21=7
M22 =\(\begin{vmatrix}5&8\\1&3\end{vmatrix}\)=15-8=7
∴A22=cofactor of a22=(−1)2+2 M22=7
M23=\(\begin{vmatrix}5&3\\1&2\end{vmatrix}\)=10-3=7
∴A23 = cofactor of a23 = (−1)2+3 M23 = −7
We know that ∆ is equal to the sum of the product of the elements of the second row
with their corresponding cofactors.
∴ ∆ = a21A21 + a22A22 + a23A23 = 2(7) + 0(7) + 1(−7) = 14 − 7 = 7
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