Question

[tex] If \left|\begin{array}{ccc}5&4&8\\x-3&-8&-16\\3&9&4 \end{array}\right| = 0 determine the value of x. [\tex]

Answer 1

Answer:

The value of x is -7

Step-by-step explanation:

$\left|\begin{array}{ccc}5&4&8\\x-3&-8&-16\\3&9&4 \end{array}\right|=0$

$\left|\begin{array}{ccc}5&4&8\\x&1&-12\\3&9&4 \end{array}\right|=0$  $R_2\implies\:R_2+R_3$

Expanding along the first row, we get

$5(4+108)-4(4x+36)+8(9x-3)=0$

$\implies\:560-16xx-144+72x-24=0$

$\implies\:56x+392=0$

$\implies\:56x=-392$

$\implies\:x=\frac{-392}{56}$

$\implies\:\boxed{\bf\:x=-7}$