If $$x=$$α, $$y=$$β, $$z=$$γ is the solution, for the system of equations $$2x$$−$$y+8z=13$$, $$3x+4y+5z=18$$, $$5x$$−$$2y+7z=20$$. Then αβ$$+$$βγ$$+$$γα$$=$$

Question

If $$x=$$α,  $$y=$$β, $$z=$$γ is the solution, for the system of equations $$2x$$−$$y+8z=13$$,  $$3x+4y+5z=18$$,  $$5x$$−$$2y+7z=20$$. Then αβ$$+$$βγ$$+$$γα$$=$$

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Augmented matrix $$AD=2-1813345185-2720$$                                                $$R2$$→$$2R2-3R1$$, $$R3$$→$$2R3-5R1$$                                             ~$$2-1813011-14-301-26-25$$                                                 $$R1$$→$$11R1+R2$$,  $$R3$$→$$11R3-R2$$                                             ~$$22074140011-14-300-272-272$$                                                 $$R1$$→$$R12$$ , $$R2$$→$$R2-272$$                                             ~$$1103770011-14-30011$$                                                 $$R1$$→$$R1-37R3$$, $$R2$$→$$R2+14R3$$                                             ~$$1100330110110011$$ The above system is equivalent to $$11x=33$$, $$11y=11$$, $$z=1$$. ⇒$$x=3$$, $$y=1$$ and $$z=1$$ ⇒α$$=3$$, β$$=1$$ and γ$$=1$$ ∴ αβ$$+$$βγ$$+$$γα$$=7$$

System of linear equations

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If $x = α, y = β, z = γ$ is the solution, for the system of equations $2 x - y + 8 z = 13, 3 x + 4 y + 5 z = 18, 5 x - 2 y + 7 z = 20$ . Then $α β + β γ + γ α =$

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System of linear equations

Remember concepts with our Masterclasses.

If x=α, y=β, z=γ is the solution, for the system of equations 2x−y+8z=13, 3x+4y+5z=18, 5x−2y+7z=20. Then αβ+βγ+γα=

Ready to Test Your Skills?

free study material

If $x = α, y = β, z = γ$ is the solution, for the system of equations $2 x - y + 8 z = 13, 3 x + 4 y + 5 z = 18, 5 x - 2 y + 7 z = 20$ . Then $α β + β γ + γ α =$