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  • Please solve rd sharma class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 1 maths textbook solution

Please solve rd sharma class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 1 maths textbook solution

Answers (1)

Answer:

            x=y=z=0

Hint:

If \left | A \right |\neq 0, then  x=y=z=0  is the only solution of the homogeneous system.

Given:

            2x-y+z=0

            3x+2y-z=0

            x+4y+3z=0

Explanation:

The given homogeneous system can be written in matrix form

i.e.    \begin{bmatrix} 2 & -1 &1 \\ 3& 2 &-1 \\ 1& 4 &3 \end{bmatrix}\begin{bmatrix} x\\ y\\ z\end{bmatrix} = \begin{bmatrix} 0\\ 0\\ 0\end{bmatrix}

        A= \begin{bmatrix} 2 & -1 &1 \\ 3& 2& -1\\ 1& 4 & 3 \end{bmatrix}

Let

        A= \begin{vmatrix} 2 & -1 &1 \\ 3& 2& -1\\ 1& 4 & 3 \end{vmatrix}

=2(6+4)+1(9+1)+1(12-2)

=20+10+10

=40

\left | A \right |\neq 0

So the given system of equations has a trivial solution.

x=0, y=0, z=0

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