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  • Need solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 7

Need solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 7

Answers (1)

Answer:

Correct option (a)

Hint:

First solve these determinants, then find conclusion.

Given:

        \Delta _{1}=\begin{vmatrix} 1 &1 &1 \\ a &b &c \\ a^{2} &b^{2} &c^{2} \end{vmatrix},\: \: \Delta _{2}=\begin{vmatrix} 1 &bc &a \\ 1 &ca &b \\ 1 &ab &c \end{vmatrix}

Solution:

Here,

        \Delta _{1}=\begin{vmatrix} 1 &1 &1 \\ a &b &c \\ a^{2} &b^{2} &c^{2} \end{vmatrix}

                =bc^{2}-b^{2}c-(ac^{2}-a^{2}c)+ab^{2}-a^{2}b

                =bc^{2}-b^{2}c-ac^{2}+a^{2}c+ab^{2}-a^{2}b

        \Delta _{2}=\begin{vmatrix} 1 &bc &a \\ 1 &ca &b \\ 1 &ab &c \end{vmatrix}

                =c^{2}a-ab^{2}-bc(c-b)+a(ab-ac)

                =c^{2}a-ab^{2}-bc^{2}+bc^{2}+a^{2}b-a^{2}c

                =-(bc^{2}-b^{2}c-ac^{2}+a^{2}c+ab^{2}-a^{2}b)

        \Rightarrow \Delta _{1}=-\Delta _{2}

        \Rightarrow \Delta _{1}+\Delta _{2}=0

Hence, option (a) is correct.

Posted by

Gurleen Kaur

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