Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B ={1 + x − 2x^2 , −1 + x
Let P2(R) be the vector space of polynomials over R up to degree 2. Consider B ={1 + x − 2x^2 , −1 + x + x^2, 1 − x + x^2}, B’ ={1 − 3x + x^2, 1 − 3x − 2x^2, 1 − 2x + 3x^2}. (a) Show that B and B’ are bases of P2(R). (b) Find the coordinate matrices of p(x) = 9x^2 + 4x − 2 relative to the bases B and B’. (c) Find the transition matrix P_B=→B’ (d) Verify that, [x(p)]B’= P_B→B’ [x(p)B].
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