LINEAR ALGEBRA EXERCISE (4) Let C[-2, 2] denote the vector space of continuous functions f [-2,2] → R, equipped with the inner product (f.g) = f* f(t)g(t)dt. -2 Let P₁ be the space of the polynomials of degree at most one in t, and g(t) = t³. Compute Projp, (9), the orthogonal projection of g(t) into P₁, with respect to the inner product (-,-).

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Q: i) Determine the linear mapping T : R3 → R² which maps the basis vectors {(1,0,0), (0, 1,0), (0,0,…

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Q: Linear Algebra: Consider the polynomials p1(t)=1+t^2, p2(t)=t, p3(t)=t−t^2. Is {p1,p2,p3} a…

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Q: ii) Two subspaces of R3 are U = {(x,y, z) : x – 3y – 2z = 0} and W = %3D {(r, y, z) : x – y = 0}.…

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Q: let V = M2x2 (R) M = { A € V A = A} N = {AEV A = -A²} Subset of the vector space V The answer must…

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Q: The function f : R? → R given by f(x, y) = x² + 2y is a linear transformation. O True O False

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