Given $$2x$$−$$y+2z=2$$, x−$$2y+z=$$−$$4$$, $$x+y+$$λ$$z=4$$, then the value of λ such that the given system of equations has no solution is

Question

Given $$2x$$−$$y+2z=2$$, x−$$2y+z=$$−$$4$$, $$x+y+$$λ$$z=4$$, then the value of λ such that the given system of equations has no solution is

Infinity Learn · Accepted Answer

The condition for a $$non-homogeneous$$ system to have a no solution is rankA≠rankAD Now, augmented matrix $$AD=2-1221-21-411$$λ$$4$$                                                           $$R2$$→$$2R2-R1$$, $$R3$$→$$2R3-R1$$                                                      ~$$2-1220-30-10032$$λ$$-26$$                                                          $$R3$$→$$R3+R2$$                                                      ~$$2-1220-30-10002$$λ$$-2-4$$ If $$2$$λ$$-2=0$$, then $$rankA=2$$,$$rankAD=3$$ so that rankA≠rankAD. ∴$$2$$λ$$-2=0$$⇒λ$$=1$$

Given $2 x - y + 2 z = 2, x - 2 y + z = - 4, x + y + λ z = 4$ , then the value of $λ$ such that the given system of equations has no solution is

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Given 2x−y+2z=2, x−2y+z=−4, x+y+λz=4, then the value of λ such that the given system of equations has no solution is

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Given $2 x - y + 2 z = 2, x - 2 y + z = - 4, x + y + λ z = 4$ , then the value of $λ$ such that the given system of equations has no solution is