LA2.1.6

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Find the value of determinant of the matrix {\begin{bmatrix}29&26&22\\25&31&27\\63&54&46\end{bmatrix}}\,

Determinant is

{\begin{vmatrix}29&26&22\\25&31&27\\63&54&46\end{vmatrix}}\,

By C_{1}-C_{2},C_{2}-C_{3}\,(C1,C2 etc.are respective columns)

{\begin{vmatrix}3&4&22\\-6&4&27\\9&8&46\end{vmatrix}}\,

(3)(4){\begin{vmatrix}1&1&22\\-2&1&27\\3&2&46\end{vmatrix}}\,

By C_{1}-C_{2},C_{3}-22C_{2}\, we get

12{\begin{vmatrix}0&1&0\\-3&1&5\\1&2&2\end{vmatrix}}\,

Therefore the determinant is 12(-1)(-6-5)=132\,


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