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  • Provide solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 26

Provide solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 26

Answers (1)

Answer:

Correct option (d)

Hint:

Evaluate the given determinant by applying row or column operation.

Given:

Let\; \; \; \; \Delta =\begin{vmatrix} b^{2}-ab &b-c &bc-ac \\ ab-a^{2} &a-b &b^{2}-ab \\ bc-ca &c-a &ab-a^{2} \end{vmatrix}

We have to find the value of \Delta

Solution:

Here\; \; \; \; \Delta =\begin{vmatrix} b^{2}-ab &b-c &bc-ac \\ ab-a^{2} &a-b &b^{2}-ab \\ bc-ca &c-a &ab-a^{2} \end{vmatrix}

        \Rightarrow \Delta =\begin{vmatrix} b(b-a) &b-c &c(b-a) \\ a(b-a) &a-b &b(b-a) \\ c(b-a) &c-a &a(b-a) \end{vmatrix}

Taking common (b-a) from column 1 and 3

        \Rightarrow \Delta=(b-a)^{2}\left|\begin{array}{lll} b & b-c & c \\ a & a-b & b \\ c & c-a & a \end{array}\right|

Here, C1 and C2 are same and if any two row or column of a matrix is identical then determinant will be zero.

        \Rightarrow \Delta=\left|\begin{array}{lll} b & b & c \\ a & a & b \\ c & c & a \end{array}\right|

        \Rightarrow \Delta=0

Hence,\; \; \; \; \begin{vmatrix} b^{2}-ab &b-c &bc-ac \\ ab-a^{2} &a-b &b^{2}-ab \\ bc-ca &c-a &ab-a^{2} \end{vmatrix}=0

Posted by

Gurleen Kaur

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