Find a basis {p(x), q(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.
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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!Find a basis {p(x), q(x)} for the vector space {f(x) E P2[x] | f'(-8) = f(1)} where P2[x] is the vector space of polynomials in a with degree at most 2. You can enter polynomials using notation e.g., 5+3xx for 5 + 3x?. p(x) = , q(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|| = afgThe 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) = __ .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)
- 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.If A and B are orthogonal, is A+B also orthogonal? Can you demonstrate Algebraically using A + B = (A + B)^T etc...? Thank you.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.
- Using linear algebra, show that G={p1(x)=1−x+x^2, p2(x)=x, p3(x)=x+x^2} is a basis of P2, the vector space of polynomials of degree at most two with real coefficients.The set of all polynomials of degree 6 under the standard addition and scalar multiplication operations is not a vector space because" We can find a polynomial P(x) for which 1-P(x)=P(x) We can find two polynomials P(x) and Q(x) for which P(x)-Q(x)=Q(x)•P(x) It is not closed under addition. We can find a polynomial P(x) such that (c+d)P(x)zcP(x)+dP(x).Find the coordinate vector of [*]B= = -(1-10--- 2 with respect to the basis B = for R³.