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- 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!{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) = =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) = __ .
- Suppose 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.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|| = afgFind 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)