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Need solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 23

Answers (1)

Answer:

Correct option (c)

Hint:

If all the element in a diagonal of determinant is zero, then determinant must be zero.

Given:

Given that,

        f(x)=\begin{vmatrix} 0 &x-a &x-b \\ x+a &0 &x-c \\ x+b &x+c &0 \end{vmatrix}

We have to find  f(x)

Solution:

Here

        f(x)=\begin{vmatrix} 0 &x-a &x-b \\ x+a &0 &x-c \\ x+b &x+c &0 \end{vmatrix}

Put X=0,

        \Rightarrow f(0)=\begin{vmatrix} 0 &-a &-b \\ a &0 &-c \\ b &c &0 \end{vmatrix}

Expanding along R1

        \Rightarrow f(0)=a(0+bc)-b(ac-0)

        \Rightarrow f(0)=abc-abc

        \Rightarrow f(0)=0

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Gurleen Kaur

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