Let H={p(t) : p(t) =a+bt +ct^3; a,b,c ∈ R} (a) Show that H is a subspace of P 3 (b) Let p1. P2. P3 be polynomials in H such that p1(t)=2, p2(t) =(1+3t^3), p3(t)= -1-t-t"^3. Use coardinate vectors in order each of the following andjustify your answer each part. (I) Verify that {p1, P2, P3} form a linearly independent set in P3.  (ii)  Verify that {p1, p2, P3} does not span P3. (iii)  Can the set {p1, p2, P3} form basis for P3?

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.