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  • explain solution rd sharma class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 8 maths

explain solution rd sharma class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 8 maths

Answers (1)

Answer:

            x=y=z=0

Hint:

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

Given:

            2x+3y-z=0

            x-y-2z=0

            3x+y+3z=0

Explanation:

The given homogeneous system can be written in matrix form

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

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

Let

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

              =2(-3+2)-3(3+6)-1(1+3)

              =-2-27-4

              =-33

       \left | A \right |\neq 0

Hence, x=y=z=0

 

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