Question

Evaluate determinant-Row1-102 18 36,Row2-1 3 4,Row3-17 3 6 using property 3 and 4.Explain with detailed steps.

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ \mathrm{You}\mathrm{must}\mathrm{have}\mathrm{mentioned}\mathrm{property}3\mathrm{and}4\mathrm{so}\mathrm{here}\mathrm{is}\mathrm{the}\mathrm{general}\mathrm{solution}. \\ △=\left|\begin{array}{ccc}102& 18& 36\\ 1& 3& 4\\ 17& 3& 6\end{array}\right| \\ =\left|\begin{array}{ccc}6\times 17& 6\times 3& 6\times 6\\ 1& 3& 4\\ 17& 3& 6\end{array}\right|=6\left|\begin{array}{ccc}17& 3& 6\\ 1& 3& 4\\ 17& 3& 6\end{array}\right|\left[\mathrm{Taking}6\mathrm{common}\mathrm{from}\mathrm{row}1\right] \\ \mathrm{Now}\mathrm{row}1\mathrm{and}\mathrm{row}3\mathrm{are}\mathrm{same}\mathrm{so}\mathrm{using}\mathrm{property}\mathrm{that}\mathrm{if}\mathrm{two}\mathrm{rows}\mathrm{are}\mathrm{same}\mathrm{then}\mathrm{deter}- \\ \mathrm{minants}\mathrm{is}0. \\ =0 \\ \mathrm{Regards} \end{gathered}$$