If the system of equations $$x+2y+3z=$$λx, $$3x+y+2z=$$λy, $$2x+3y+z=$$λz has $$non-trivial$$ solution , then λ$$=$$……..

Question

If the system of equations  $$x+2y+3z=$$λx, $$3x+y+2z=$$λy, $$2x+3y+z=$$λz has $$non-trivial$$ solution , then  λ$$=$$……..

Infinity Learn · Accepted Answer

Given system of equations , $$1$$−λ$$x+2y+3z=0$$,$$3x+1$$−λ$$+2z=0$$, $$2x+3y+1$$−λ$$z=0$$ Has nontrivial solution ⇒$$1$$−λ$$2331$$−λ$$2231$$−λ$$=0R1+R2+R3$$⇒$$6$$−λ$$6$$−λ$$6$$−λ$$31$$−λ$$2231$$−λ(6$$−λ$$)11131$$−λ$$2231$$−λ$$C2$$−$$C1C3$$−$$C1$$⇒$$(6$$−λ$$)1003$$−λ−$$2$$−$$121$$−λ−$$1=0$$⇒$$(6$$−λ$$)[$$($$λ$$+1)($$λ$$+2)+1$$]$$=0$$⇒λ$$=6$$,λ$$2+3$$λ$$+3=0$$

If the system of equations $x + 2 y + 3 z = λ x, 3 x + y + 2 z = λ y, 2 x + 3 y + z = λ z$ has non-trivial solution , then $λ$ =……..

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If the system of equations x+2y+3z=λx, 3x+y+2z=λy, 2x+3y+z=λz has non-trivial solution , then λ=……..

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If the system of equations $x + 2 y + 3 z = λ x, 3 x + y + 2 z = λ y, 2 x + 3 y + z = λ z$ has non-trivial solution , then $λ$ =……..