etermine whether the following are subs 5= {fe C(R) | f(304) = 0} a subspace of C(R)? Justify your answer. S = {(1, T2, T3, T₁) € R4 | ₁-2x3 = 0, ₁ = -4x2} a subspace of R4? Justify your answer.

Q: Determine the interpolating polynomial in Newton's form that passes through the points and Use the…

A:

Q: Find a polynomial y = p(x) of degree 4 that goes through the points (0, 4), (1, 2), (2, -4), (3,…

A: solution of the given question is like this:

Q: Find the 3rd degree interpolating polynomial by Newton's backward formula X f(X) Af(X;) A²f(X;)…

A:

Q: Consider the data (1,10), (3,6)(1,10), (3,6). Then, Newton's polynomial that interpolates the data…

A: Solution of given problem is followed by Newton's interpolation formula.

Q: Find a linear funtion P(z) = a + a₁ which gives the best least squares fit for the following points:…

A: Given the points -4,0, -2, -2, 4,-9, 5, -8. Now,  x y x2 xy -4 0 16 0 -2 -2 4 4 4 -9 16 -36…

Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

A:

Q: Formulate that the Lagrange interpolation polynomial that passes through points (0, 3), (1,4) and…

A: To show that the Lagrange interpolation polynomial that passes through points (0,-3),(1,4),(2,15) is…

Q: A third degree polynomial passes through the points (0,9), (1.14), (2,17), (3,24), (4,41), (5,74)…

A: The value of X1=∆y3=y4-y3=24-17⇒X1=7and value of ∆2y2=X2=∆y3-∆y2=7-3=4⇒X2=4

Q: Determine the linear interpolating polynomial that passes through the points (2,4) and (5,1). p(x) =…

A:

Q: f(a + h) – f(a) 7. If f(x) = 3x² +9, find and simplify where h + 0. h За + 6h 3h + 12a ба + 3h 3h +…

A: Hence option (c) is correct.

Q: Interpolation is a type of estimation, a method of constructing new data points within the range of…

A: Suppose that there are three points x1,y1,x2,y2,x3,y3. The given system is:…

Q: Using Newton's Divided Difference, the interpolating polynomial of the points (xo.Yo) = (- 2,1),…

A:

Q: Find the midpoint of (6, 7) and (14, 11). O (7, 18) О 20, 18) О 10, 10) (10, 9)

A: given points :(x1,y1)=( 6,7)(x2,y2)=(14,11) Midpoint = x1+x22,y1+y22

Q: A constant temperature, pressure-volume thermodynamic process has the following data: Pressure 420…

A:

Q: 6. (10pts) Determine whether you can find the interpolating polynomial p(t) = a, + a,t + a,r² for…

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Q: 1. Sove for the orthogonal traectories Y- 3X + 1 -3X Ce

A:

Q: Given m (x) = 3x - 9 and n(x) = - 4 +2x, find 2(x) – m (x). Do not include spaces in your answer.

A: By using direct subtraction rules we can   find n(x)-m(x)

Q: Factor completely. qs - 8s + qf - 8f qs - 8s + qf - 8f =

A: We have to complete factor

Q: Why isn't R2 a subspace of R³?

A: For being a subspace a space must be a subset of the other. But here R2 is not a subset of R3. So…

Q: Find a least-squares best fit line for the points (1, 1), (2, 5), (3, 5). Write your answer as a…

A:

Q: (V10 + V5)(V10 – V5) = (_) – (P = –

A: Given, To solve

Q: -2 2 -3 Q4: Find the minimum polynomial of A=| 2 1 -6 then test the -1 -2 diagonalization of A.

A:

Q: Find y(5) if a second-degree polynomial is fitted to the data points (1, 4), (2, 6), (3, 9), (4,…

A:

Q: Let P(x) be the interpolating polynomial for the data (0, 1), (1,3), (4, -3). Then P(2) = 3 4 -3 1

A: Here are 2 ways to solve find the solution In 2 method we will use this lagrange interpolation…

Q: (3) Construct a linear spline interpolating (-1, 0), (0, 1), (1, 3).

A:

Q: The function f(x) = -X-3)2 - 4, will have a shift of 4 units to the left. O True O False

A:

Q: f(x)=x(40-x)/(20+9cos(x)) Let the function and the set V=[10,15,20,25,30]. Consider the set W of…

A: First we calculate f(x) by using value of x  Next we use Lagrange formula to calculate the…

Q: Find iterpolation polynomial p2(x) = ax² + bx + c that passess through the points: (0,7), (1,12),…

A:

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…