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Name: provide solution for rd sharma maths class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 2
Uploaded: Fri, 2021-07-16 23:16
Description: provide solution for rd sharma maths class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 2

provide solution for rd sharma maths class 12 chapter Solution of simultaneous linear equation exercise 7.2 question 2

Answers (1)

Answer:

$x=\frac{-5k}{11}, y=\frac{12k}{11}, z=k$

Hint:

If $\left | A \right |= 0$ , then the system of equation has non-trivial solution.

Given:

$2x-y+2z=0$

$5x+3y-z=0$

$x+5y-5z=0$

Explanation:

The given homogeneous system can be written in matrix form

i.e. $\begin{bmatrix} 2& -1& 2\\ 5 & 3& -1\\ 1& 5& -5 \end{bmatrix}\begin{bmatrix} x\\ y\\ z\end{bmatrix}=\begin{bmatrix} 0\\ 0\\ 0\end{bmatrix}$

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