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  • need solution for rd sharma maths class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 7

need solution for rd sharma maths class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 7

Answers (1)

Answer:

            x=y=z=0

Hint:

If \left | A \right |\neq 0, then x=y=z=0

Given:

            3x+y-2z=0

            x+y+z=0

            x-2y+z=0

Explanation:

The given homogeneous system can be written in matrix form

i.e.    \begin{bmatrix} 3 & 1 &-2 \\ 1& 1 &1 \\ 1& -2 &1 \end{bmatrix}\begin{bmatrix} x\\ y\\ z\end{bmatrix} = \begin{bmatrix} 0\\ 0\\ 0\end{bmatrix}

        A= \begin{bmatrix} 3 & 1 &-2 \\ 1& 1& 1\\ 1& -2 & 1 \end{bmatrix}

Let

        \left | A \right |= \begin{vmatrix} 3& 1 &-2 \\ 1& 1& 1\\ 1& -2 & 1 \end{vmatrix}

              =3(1+2)-1(1-1)-2(-2-1)

              =9+0+6

              =15

       \left | A \right |\neq 0

Hence, x=0, y=0, z=0

 

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