If \begin{vmatrix} y+z & x & x \\ y & z+x &y \\ z & z & x+y\end{vmatrix} =K(xyz)

Then K is equal to

  • Option 1)

    4

  • Option 2)

    -4

  • Option 3)

    0

  • Option 4)

    None

 

Answers (1)

As learnt in concept

Value of determinants of order 3 -

-

 

 \begin{vmatrix} y+z & x & x\\ y&z+x&y\\z & z& x+y \end{vmatrix}

 

\Rightarrow (y+z)(x^{2}+(y+z)x)-x (xy+y^{2}-yz)+x(yz-xz-z^{2})

\Rightarrow (y+z)^{2}x+x^{2}y+x^{2}z-x^{2}y-xy^{2}+2xyz-x^{2}z-xz^{2}

\Rightarrow 4xyz


Option 1)

4

This option is correct.

Option 2)

-4

This option is incorrect.

Option 3)

0

This option is incorrect.

Option 4)

None

This option is incorrect.

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