Using properties of determinants, solve the following for x :

x-2 2x-3 3x-4

x-4 2x-9 3x-16 =0

x-8 2x-27 3x-64

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Using properties of determinants, solve the following for x
:
x-2 2x-3 3x-4
x-4 2x-9 3x-16 =0
x-8 2x-27 3x-64

Ajanta Trivedi · Accepted Answer

the given determinant is

$| \begin{matrix} x - 2 & 2 x - 3 & 3 x - 4 \\ x - 4 & 2 x - 9 & 3 x - 16 \\ x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} | = 0$ $R_{1} \to R_{1} - R_{3} a n d R_{2} \to R_{2} - R_{3}$

$| \begin{matrix} 6 & 24 & 60 \\ 4 & 18 & 48 \\ x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} | = 0$ $R_{1} \to R_{1} / 6 a n d R_{2} \to R_{2} / 2$

$| \begin{matrix} 1 & 4 & 10 \\ 2 & 9 & 24 \\ x - 8 & 2 x - 27 & 3 x - 64 \end{matrix} | = 0$ $C_{2} \to C_{2} - 4 C_{1} a n d C_{3} \to C_{3} - 10 C_{1}$

$| \begin{matrix} 1 & 0 & 0 \\ 2 & 1 & 4 \\ x - 8 & - 2 x + 5 & - 7 x + 16 \end{matrix} | = 0$

i.e. $(- 7 x + 16) - 4 (- 2 x + 5) = 0$

$- 7 x + 16 + 8 x - 20 = 0 x - 4 = 0 \Rightarrow x = 4$

hope this helps you.

Using properties of determinants, solve the following for x : x-2 2x-3 3x-4 x-4 2x-9 3x-16 =0 x-8 2x-27 3x-64

Using properties of determinants, solve the following for x :

x-2 2x-3 3x-4

x-4 2x-9 3x-16 =0

x-8 2x-27 3x-64