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  • Please solve rd sharma class 12 chapter determinants exercise 5.5 question 2 maths textbook solution

Please solve rd sharma class 12 chapter determinants exercise 5.5 question 2 maths textbook solution

Answers (1)

Answer: x = 0, y = 0, z = 0.

Hint:  If \left | A \right |\neq 0 then the homogeneous system has trivial solutions.

Given:

2x + 3y + 4z =0

x + y + z = 0

2x + 5y - 2z = 0

Solution:

The above linear equations can be represented in matrix form i.e.

            A=\begin{bmatrix} 2 & 3&4 \\ 1& 1 & 1\\ 2& 5 & -2 \end{bmatrix}, X =\begin{bmatrix} x\\ y \\ z \end{bmatrix}, B = \begin{bmatrix} 0\\ 0\\ 0\end{bmatrix}

                            (or)  AX = B

Now,

        \left | A \right | = \begin{vmatrix} 2 & 3& 4\\ 1& 1 &1 \\ 2& 5& -2\end{vmatrix}

 

              = 2(-2 - 5) - 3(-2 -2) + 4(5 -2)

              = -14 + 12 + 12

              = 10 \neq 0

Hence,

        x = 0, y = 0, z = 0.

Posted by

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