Question

6. 10 Suppose a cubic polynomial y2does through the points ( i) fori-1,2,3, 4, where i j for i,j 1,2,3, 4 and i j a) 2 Find the system of equations that determines the coefficients a, b, c and d (b) |6 Find the determinant of the coefficiant matrix using row operations, and show that the coefficient matrix is invertible. Note that you will receive no mark if you compute the determinant using cofactor expansion. (c) [2| Is it possible that no such cubic functions exist? Is it possible that there exist more than one such cubic function? Justify your answer

Answer 1

and it a rt_b.t.qǐ.c-r u d 2 y 1 211 M. 3 しち der (A): 3 左n, ''s.nu. 沓亡 訓2

R, 2

C) since det(a) o ran.