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- {ƒf(x) = P₂[x] |ƒ'(−8) =ƒ(1)} where P₂[x] is the vector space of polynomials in x with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5 + 3x². p(x) = ,q(x) = =Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the equation r1(t)=r2(t) may not produce all the points where the graphs of these functions intersect. Please Provide Unique Answer. Thank you!The functions f(x) = x2 and g(x) = 5x are "vectors" in F. This is the vector space of all real functions. (The functions are defined for -oo < x < oo.) The combination 3f(x) - 4g(x) is the function h(x) = __ .
- Use the inner product (f, 9) = | f(2)g(x) da in the vector space P(R) of polynomials to find (f, g), || f|| ||g||, and the angle afg between f(æ) and g(x) for 2 f(x) = 10x – 3 and g(x) = -9x + 10. (f, 9) = || F|| = l|g|| = afgSuppose y1 ( x), y2 ( x), y3 ( x) are three different functions of x. The vector space they span could have dimension 1, 2, or 3. Give an example of y1, y2, y3 to show each possibility.Find a basis {p(x), q(x)} for the vector space {f(x) = P₂[x] | f'(-3) = f(1)} where P₂[x] is the vector space of polynomials in x with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5 + 3x². p(x) = , q(x) =
- Find a basis {p(x), g(x)} for the vector space {f(x) = P₂[x] | ƒ'(3) = f(1)} where P₂ [x] is the vector space of polynomials in x with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5 + 3x². p(x) = q(x) =A real-valued function f defined on the real line is called an even function if J( -t) = f (t) for each real number t. Prove that the set of even functions defined on the real line with the operations of addition and scalar multiplication is a vector space.Find a basis {p(x), q(x)} for the vector space {f(x) e P2[x] | f' (7) = f(1)} where P2[x] is the vector space of polynomials in x with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5 + 3x. p(x) = q(x)
- Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by the vectors (-3,7) and (9,3). (Use symbolic notation and fractions where needed. Give your answer in the form (*, *).) G(u, v) =Use Lagrange Polynomials to find a cubic curve that goes through the points {(0,-3), (1,0), (2,5), (3,18)}Find the coordinate vector of p(x) in P,, relative to the basis S= {p,.P;. P;}. where p(x) = 3+6x-10x, p, (x) = 2- 4x, p; (x) = x+ 3x, p;(x) = 4+ 6x² 5) (10)