Let I ≤ k [x1,...,xn] be an ideal. a. Prove that I₁ = Ink[x1+1, ..., Xn] is an ideal of k[x1+1, . . . ‚ Xn]. b. Prove that the ideal 11+1 C k[X1+2,...,xn] is the first elimination ideal of I, C k[x1+1, … … …, Xn]. This observation allows us to use the Extension Theorem multiple times when eliminating more than one variable. . . .