Evaluate \(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\).(a) -6(b) -34(c) 34(d) 22The question was asked at a job interview.This intriguing question originated from Determinant topic in section Determinants of Mathematics – Class 12

Evaluate \(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\).(a) -6(

1.	Evaluate \(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\).(a) -6(b) -34(c) 34(d) 22The question was asked at a job interview.This intriguing question originated from Determinant topic in section Determinants of Mathematics – Class 12
Answer» RIGHT OPTION is (b) -34 To explain I would say: ∆=\(\BEGIN{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\) Expanding along the first ROW, we get ∆=1\(\begin{vmatrix}4&5\\2&1\end{vmatrix}\)-1\(\begin{vmatrix}3&5\\-1&1\end{vmatrix}\)-2\(\begin{vmatrix}3&4\\-1&2\end{vmatrix}\) =1(4-5(2))-1(3-5(-1))-2(6-4(-1)) =(4-10)-(3+5)-2(6+4) =-6-8-20=-34.

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