Without expanding, show that $\left| \begin{smallmatrix} 3&4&5 \\ 15&21&26 \\ 21&29&36 \\ \end{smallmatrix}\right|=0$

Question

Without expanding,prove that: $$\left| \begin{matrix} 3&4&5 \\ 15&21&26 \\ 21&29&36 \\ \end{matrix}\right|=0$$

My Attempt:

$$L.H.S.= \begin{vmatrix} 3 & 4 & 5 \\ 15 & 21 & 26 \\ 21 & 29 & 36 \\ \end{vmatrix} $$ Packing common "$3$" from the first column: $$=3 \begin{vmatrix} 1 & 4 & 5 \\ 5 & 21 & 26 \\ 7 & 29 & 36 \\ \end{vmatrix} $$

Answer 1

Row3=Row2+2*Row1. Hence, determinant is zero.

Answer 2

Great start! The next thing you want to look at is a single column operation, which should give you the result straight away.