Let P, have the inner product given by evaluation at -2, - 1, 1, and 2. Let po (t) = 1, p, (t) = 2t, and p2 (t) = r*. a. Compute the orthogonal projection of p, onto the subspace spanned by Po and p,. b. Find a polynomial q that is orthogonal to Po and p,, such that (Po.P1.9, is an orthogonal basis for Span(Po P,.P2}. Scale the polynomial q so that its vector of values at (-2, - 1,1,2) is (1, - 1,- 1,1). a. P2 = (Simplify your answer.)

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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.