Partial fraction decomposition case

Question

Questions:

Partial Fraction Decomposition Case

Let a₁, a₂,..., a_n be n distinct numbers and set f(x)= 1/(x-a₁)(x-a₂)^...x-a_n).

An identityf(x) = c₁/x-a₁+c₂/x-a₂+...+c_n/x-a_n

is called a partial fraction decomposition of f(x).

i. Show that the preceding identity is equivalent to a nonhomogeneous system of n linear equations in the variable c₁, c₂,...,c_n

ii. Show that the system of homogeneous equations corresponding to the preceding identity has a unique solution, thus a unique partial fraction decomposition for f(x) is guaranteed.