Statement $$-$$ I : The system of equations $$x+y+z=6$$,x−$$y+z=2$$,$$2x$$−$$y+3z=9$$ has unique solution statement $$-II$$ : The system of equations $$x+y+z=1$$,$$2x+y+z=2$$,$$x+2y+2z=1$$ has no solution

Question

Statement $$-$$ I : The system of equations $$x+y+z=6$$,x−$$y+z=2$$,$$2x$$−$$y+3z=9$$     has unique solution   statement $$-II$$ : The system of equations $$x+y+z=1$$,$$2x+y+z=2$$,$$x+2y+2z=1$$     has no solution

Infinity Learn · Accepted Answer

Statement : I[AB]$$=11161$$−$$1122$$−$$139R2$$−$$R1R3$$−$$2R1$$~$$11160$$−$$20$$−$$40$$−$$31$$−$$3$$~$$11160$$−$$20$$−$$400262R3$$−$$3R2$$⇒ unique solutionsStatement : II Since, [AB]$$=111121121221$$   $$R2$$→$$R2$$−$$2R1R3$$→$$R3$$−$$R1$$ ~  $$11110$$−$$1$$−$$100110R3$$→$$R3+R2$$  ~  $$11110$$−$$1$$−$$100000Rank$$ $$AB=$$ Rank A<$$3$$, Infinitely solutions

Statement - I : The system of equations $x + y + z = 6, x - y + z = 2, 2 x - y + 3 z = 9$ has unique solution
statement -II : The system of equations $x + y + z = 1, 2 x + y + z = 2, x + 2 y + 2 z = 1$ has no solution

Unlock the full solution & master the concept.

Ready to Test Your Skills?

free study material

Statement - I : The system of equations x+y+z=6,x−y+z=2,2x−y+3z=9 has unique solution statement -II : The system of equations x+y+z=1,2x+y+z=2,x+2y+2z=1 has no solution

Unlock the full solution & master the concept.

Ready to Test Your Skills?

free study material

Statement - I : The system of equations $x + y + z = 6, x - y + z = 2, 2 x - y + 3 z = 9$ has unique solution
statement -II : The system of equations $x + y + z = 1, 2 x + y + z = 2, x + 2 y + 2 z = 1$ has no solution