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  • Need solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 11

Need solution for RD Sharma maths class 12 chapter Determinants exercise multiple choise question 11

Answers (1)

Answer:

Correct option (d)

Hint:

Put x=0 in the determinant and then check the skew-symmetric.

Given:

            \begin{vmatrix} 0 &x^{2}-a &x^{3}-b \\ x^{2}+a &0 &x^{2}+c \\ x^{4}+b &x-c &0 \end{vmatrix}=0

Solution:

            \begin{vmatrix} 0 &x^{2}-a &x^{3}-b \\ x^{2}+a &0 &x^{2}+c \\ x^{4}+b &x-c &0 \end{vmatrix}

If we put x=0 in the above determinant

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

        \Rightarrow A^{T}=\begin{vmatrix} 0 &a &b \\ -a &0 &-c \\ -b &c &0 \end{vmatrix}

        \Rightarrow =\begin{vmatrix} 0 &-a &-b \\ a &0 &c \\ b &-c &0 \end{vmatrix}=-A

        \Rightarrow A^{T}=-A

Hence matrix is skew symmetric

Hence value of x is 0.

Posted by

Gurleen Kaur

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