Given a vector of coefficients a = (al, a 2, a3, a4, a5, a 6)...

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Given a vector of coefficients a → = (al, a 2, a3, a4, a5, a 6) E R 6, we define the following piecewise-linear function (with domain [0,1]): PW [a →] (x) = {a1x+a 20≤x < 1/3a3x+a41/3 (A) (10 points) The set PL = {PW[ä](r) | á ≤ R}, that is, all possible piecewise-linear functions defined with the formula above, is a vector space. (B) (10 points) The subset PLC = {PW|al(z) | PW is continuous} is a vector subspace of PL. Given a vector of coefficients a → = (al, a 2, a3, a4, a5, a 6) E R 6, we define the following piecewise-linear function (with domain [0,1]): PW [a →] (x) = {a1x+a 20≤x < 1/3a3x+a41/3 (A) (10 points) The set PL = {PW[ä](r) | á ≤ R}, that is, all possible piecewise-linear functions defined with the formula above, is a vector space. (B) (10 points) The subset PLC = {PW|al(z) | PW is continuous} is a vector subspace of PL.

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