If the values of λfor which the system of linear equations $$2x1$$−$$2x2+x3=$$λ$$x1$$, $$2x1$$−$$3x2+2x3=$$λ$$x2$$ ,−$$x1+2x2=$$λ$$x3$$ has non – trivial solution are λ$$1$$,λ$$2$$,λ$$3then$$ λ$$12+$$λ$$22+$$λ$$32/1000=$$

Question

If the values of λfor which the system of linear equations $$2x1$$−$$2x2+x3=$$λ$$x1$$, $$2x1$$−$$3x2+2x3=$$λ$$x2$$ ,−$$x1+2x2=$$λ$$x3$$ has non – trivial solution are λ$$1$$,λ$$2$$,λ$$3then$$ λ$$12+$$λ$$22+$$λ$$32/1000=$$

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The system has a non – trivial solution⇒Δ$$=0$$ ⇒$$2$$−λ−$$212$$−$$3$$−λ$$2$$−$$12$$−λ$$=0$$ ⇒$$2$$−λλ$$3+$$λ$$-4+2-2$$λ$$+2+14-3+$$λ$$=0$$ ⇒$$2$$−λλ$$2+3$$λ$$-4-4$$λ$$+4+1-$$λ$$=0$$ ⇒$$2$$λ$$2+6$$λ$$-8-$$λ$$3-3$$λ$$2+4$$λ$$-5$$λ$$+5=0$$ ⇒λ$$3+$$λ$$2-5$$λ$$+3=0$$ ⇒λ$$-1$$λ$$2+2$$λ$$-3=0$$ ⇒λ$$-1$$λ$$-1$$λ$$+3=0$$ ⇒λ$$=1$$,$$1$$,$$-3=$$λ$$1$$, λ$$2$$,λ$$3say$$ ∴λ$$12+$$λ$$22+$$ λ$$321000=1+1+91000=111000=0.011$$

System of linear equations

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If the values of $λ$ for which the system of linear equations $2 x_{1} - 2 x_{2} + x_{3} = λ x_{1}, 2 x_{1} - 3 x_{2} + 2 x_{3} = λ x_{2}, - x_{1} + 2 x_{2} = λ x_{3}$ has non – trivial solution are $λ_{1}, λ_{2}, λ_{3}$ then $(λ_{1}^{2} + λ_{2}^{2} + λ_{3}^{2}) / 1000 =$

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System of linear equations

Remember concepts with our Masterclasses.

If the values of λfor which the system of linear equations 2x1−2x2+x3=λx1, 2x1−3x2+2x3=λx2 ,−x1+2x2=λx3 has non – trivial solution are λ1,λ2,λ3then λ12+λ22+λ32/1000=

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free study material

If the values of $λ$ for which the system of linear equations $2 x_{1} - 2 x_{2} + x_{3} = λ x_{1}, 2 x_{1} - 3 x_{2} + 2 x_{3} = λ x_{2}, - x_{1} + 2 x_{2} = λ x_{3}$ has non – trivial solution are $λ_{1}, λ_{2}, λ_{3}$ then $(λ_{1}^{2} + λ_{2}^{2} + λ_{3}^{2}) / 1000 =$