Find the values of x, if [(1, 2x, 4x) (1, 4, 16) (1, 1, 1)] =0

Question

Find the values of x, if

\(\begin{vmatrix}1&2x&4x\\1&4&16\\1&1&1\end{vmatrix}=0\)

[(1, 2x, 4x) (1, 4, 16) (1, 1, 1)] = 0

Answer 1

\(\begin{vmatrix}1&2x&4x\\1&4&16\\1&1&1\end{vmatrix}=0\)

⇒ 1(4 – 16) – 2x(1 – 16) + 4x(1 – 4) = 0 

⇒ 1(-12) – 2x(-15) + 4x(-3) = 0 

⇒ -12 + 30x – 12x = 0 

⇒ 18x = 12

⇒ x = 12/18 = 2/3