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

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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