A Vandermonde matrix is an m x n matric of the form show that the columns of a Vandermonde matrix are linearly independent if the numbers are distinct.

1 t₁ t₁² t₁ⁿ⁻¹
1 t₂ t₂² t₂ⁿ⁻¹
V = . . .
. . . .
. . . .
1 tₘ tₘ² tₘⁿ⁻¹

where t₁, t₂, ... tₘ are numbers.
We will assume that these numbers are distinct, different from each other.
Multiplying an n-vector c by the Vandermonde matrix V is the same as evaluating the polynomial of degree less than n, with coefficients c₁, , cₙ at the points t₁,...,tₘ.
Show that the columns of a Vandermonde matrix are linearly independent if the numbers t₁,...,tₘ are distinct, i. e., different from each other. Hint. Use the following fact from algebra: If a polynomial p with degree less than n has n or more roots (points t for which p(t) = 0) then all its coefficients are zero.