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Determine a polyomial p of degree smaller or equal to three that fulfills p(-1) 2 p(0)- 6, p(24 a...
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3 0 7 0 3 5 [51 [51 a) Find a basis for the row space Row(A) of A (b) Find a basis for the column space Col(A) of A (c) Find a basis space d) Find the rank Rank(A) and the nullity of A (e) Determine if the vector v (1,4,-2,5,2) belongs to the null space of A. - As always,[5 is for the...
+ Question Details 2 1 , and A = | V1 V2 V3 | . Is p in Nul A? Let v,-| 0 2 Yes, p is in Nul A No, p is not in Nul A 5.+ Question Details 2 2 10 2 1 0 30 0 2 41 4 2 16 3 Let A so that an echelon form of A is given by . Find a basis for Col A 1 0 3 1 0 0 0...
$24 $6 Show that AR = P by definition. 2. 3. The firm faces a fixed cost of $2 per week, and the following variable costs. Complete the table below. Profit MR. Quantity of output (Q) TR ($) MC (S) TC (S) vC (S) FC ($) ($) ($) 0 2 2 0 6 10 8 2 1 12 2 12 10 2 2 18 15 13 3 24 19 17 30 5 24 22 36 6 30 28 2 6...
6. For the following matrix, (6 pts each) 1 2 0 2 57 A = -2 -5 1-1 10 0 -3 3 4 0 a. Determine the basis for the row space of A. b. Determine the basis for the column space of A.
er Lagrange ,Divided difference and Hermitewatnejed, Jnp 1.5, and x2-2, andf (x)ssin(x) * Given the point sx.-1, a) Find its Lagrange interpolation P on these points b) Write its newton's divided difference P, polynomial c)Write Hermite Hs by Using part a outcomes d) Write Hermite Hi by Using part b outcomes Rules: Lagrange form of Hermite polynomial of degre at most 2n-+1 Here, L., (r) denotes the Lagrange coefficient polynomial of degree n. If ec la.bl, then the error formula...
Please answer problem 4, thank you.
2. The polynomial p of degree n that interpolates a given function f at n+1 prescribed nodes is uniquely defined. Hence, there is a mapping f -> p. Denote this mapping by L and show that rl Show that L is linear; that is, 3. Prove that the algorithm for computing the coefficients ci in the Newton form of the interpolating polynomial involves n long operations (multiplications and divisions 4. Refer to Problem 2,...
3. Determine if each set is a subspace of the space of degree < 2 polynomials. If so, provide a basis for the set. (a) Degree s 2 polynomial functions whose degree 1 coefficient is zero: $(x) = ax2 + c where a,CER. (b) Degree s 2 polynomial functions whose degree 1 coefficient is 1: f(x) = ax2 + x + c where a,CER.
With explanation!
3. Let B2 be the linear operator B2f (x):- f(0)2 2 (1f (1)2, which maps functions f defined at 0, 1 to the quadratic polynomials Pa. This is the Bernstein operator of degree 2, Let T = B21Py be the restriction of B2 to the quadratics. (a) Find the matrix representation of T with respect to the basis B = [1,2,2 (b) Find the matrix representation of T with respect to the basis C = (1-x)2, 22(1-2),X2]. (c)...
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5), (2, 0, −3), (1, 2, 8), (−2, −1, 10), (−1, 0, 5
Using Lagrange interpolation, find degree two interpolating polynomial if following points are known (0, 1, 5), (2, 0, −3), (1, 2, 8), (−2, −1, 10), (−1, 0, 5) (2,3,1)