The objective of this problem is to write a polynomial p(x) = a + bx + cx2 in the form of p(x) = k1 +k2(1−x)+k3(1−2x)(1−3x). (a) Describe how would you construct a matrix for this purpose. Use E = {1, x, x2}. (b) Write p1(x) = 1 − 2x + 3x^2 in the desired form. (c) Write p2(x) = 3 + 2x − 5x2 in the desired form.

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