a) Consider three points

(x_(1),y_(1)),(x_(2),y_(2))

and

(x_(3),y_(3))

in a

2D

plane where

x_(1)

,\

x_(2)

and

x_(3)

are distinct. Show that they lie on some curve with equation\

y=a+bx+cx^(2)

for some scalars

a,b

and

c

.\ b) Find the condition of

c_(1)

in terms of

c_(2)

and

c_(3)

such that the following linear\ system is solvable:\

([1,-1,-1],[4,-2,2],[-3,1,-3])([x],[y],[z])=([c_(1)],[c_(2)],[c_(3)])

a) Consider three points (x1,y1),(x2,y2) and (x3,y3) in a 2D plane where x1, x2 and x3 are distinct. Show that they lie on some curve with equation y=a+bx+cx2 for some scalars a,b and c. 1 b) Find the condition of c1 in terms of c2 and c3 such that the following linear system is solvable: 143121123xyz=c1c2c3