Question

4. Find the real values of r for which the
System of linear equations has a non-trivial
Also find the non-trivial solutions
2x - 2y + 3z = 0
x+ry + 2z = 0
2x + rz=0 [REE 2000
Solve for x the equation sinin​

Answer 1

Answer:

Find the real values of r which the following system of linear equations has a non-trivial solution. Also find the non-trivial solutions:

2rx−2y+3z=0x+ry+2z=02x+rz=0

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Answer

△=0⇒r

3

−2r−4=0⇒(r−2)(r

2

+2r+2)=0

∴r=2 as other factor gives imaginary roots. Putting r=2, the equation reduces to 4x−2y+3z=0,x+2y+2z=0 and x+z=0

Putting x+z=0, they reduce to x−2y=0,2y+z=0 and x+z=0.

Choosing x=k, we get y=

2

k

,z=−k which given the required solutions.