#### Provide solution for RD Sharma maths Class 12 Chapter 5 Determinants Exercise VSQ Question 30 maths textbook solution.

Hint: Here we use basic concept of determinant of matrix

Given:  $\left|\begin{array}{lll} 2^{2} & 2^{3} & 2^{4} \\ 2^{3} & 2^{4} & 2^{5} \\ 2^{4} & 2^{5} & 2^{6} \end{array}\right|$

Solution :

In 1st row let's take $2^{2}$  common

In 2nd row let's take $2^{3}$  common

In 3rd row let's take $2^{4}$  common

$=\left(2^{2} \times 2^{3} \times 2^{4}\right) \times\left|\begin{array}{lll} 1 & 2 & 2^{2} \\ 1 & 2 & 2^{2} \\ 1 & 2 & 2^{2} \end{array}\right|$

Let's take 2 common from 2nd column

$=\left(2^{2+3+4+1}\right) \times\left|\begin{array}{lll} 1 & 1 & 2^{2} \\ 1 & 1 & 2^{2} \\ 1 & 1 & 2^{2} \end{array}\right|$

\begin{aligned} &=2^{10} \times 0 \quad\left[\begin{array}{l} \text { Because two column are similar, } \\ \text { So, according to property of determinant, } \\ \text { it's determinant is zero } \end{array}\right] \\ &=0 \end{aligned}

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