If the system of equations x+y+z=5, x+2y+3z=9, x+3y+αz=β has infinitely many solutions, then β3−α3=

Augmented matrix =111     1152393αβ     R2→R2−R1, R3→R3−R1                                       ~1115012402α-1β-5  R3→R3-2R2~1115012400α-5β-13System has many solutions⇒α-5=0 and β-13=0.⇒  α = 5,β=13∴  β3−α3=133−53=2072