# Show that the determinant of this system is different from zero.

**Question description**

Show that a polynomial P_n(x) of degree n that vanishes (i.e., equals 0) at

n + 1 distinct points x_0, x_1, x_2, ..... x_n must be identically zero as follows:

write the equations P_n(x_i) = 0 for i = 0, 1, 2, ....,n as a (n + 1)by(n + 1)

linear system of algebraic equations with a zero right-hand side, and show

that the determinant of this system is dierent from zero.

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