please help me with all question 10 p der the ring of polynomials Zaler), and let...
10. Camider the ring of plynicanials z,Ir, and let/ denote the elmmont r4 + 2a + 1 a) (5 points) Show that the quotient rga)/ () is a field. b) (5 points) Let a denote the coset z()Regarding F as a vector space over Z2, find a basis for F coasisting of powers of a c) (5 poluts) How nuany elements dors F have? Justify your answer. d) (5 points) Compute the product afas t a) i.e. expand this product...
7. Let V = Pa(R), the vector space of polynomials over R of degree less than 2, with inner product Define φ E p by φ(g)-g(-1) a) By direct calculation, find f e V such that (S)-dg). You are given that A 1, V3-2v) is an orthonormal basis for V (you do not need to check this). b) Find the same f as in part a, using the formula for A(6) from class.
7. Let V = Pa(R), the vector...
Thee part question. Please answer all parts!
Let E be a field of characteristic p > 0 (we proved p must always be prime). Verify that the ring homomorphism X : Z → E determined by sending χ : 1-1 E (the unity in E) ( so x(n)-n 1E wheren1E 1E 1E (n-times), x(-n)- nle for any n 1,2,3,... and X(0) 0E by definition of χ) is in fact a ring homomorphism with ker(X) = pZ. Úse the fundamental homomorphism...
This is a MATLAB question so please answer them with MATLAB
steps.
Let f(z) = V3z sin(#) and P(z) =r-x-1. 1. Find f(e) 2. Find the real solution(s) to Px) 0. Hint: use the roots command. 3. Find the global minimum for f(x). Hint: plot f over [0,2] 4. Solve f()P. Hint: plot f and P over [0,21. 5. Find lim,→0+ f(x). Hint: make a vector hi make a table [x + h; f(x + h)]". 6. Find '(In 2)....
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P
rty. I 5. [16...
Please help for Question 10A.1
MATH 270 SPRING 2019 HOMEWORK 10 10A. 1. Let S be the subspace in R3 spanned by21.Find a basis for S 2. Using as the inner product (5) ( p. 246) in section 5.4 for Ps where x10, x2 -1, x3 - 2: Find the angle between p (x) = x-3 and q(x) = x2 + x + 2. b. Fnd the vector projection of p(x) on q(x) In Cl-π, π} using as an inner...
Question 1 (10 points] Let L be the line passing through the point P=(4, -2,5) with direction vector d=[5, 2, 2]', and let T be the plane defined by –2x-3y=z=-5. Find the point Q where L and T intersect. Q=(0,0,0)
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1. A module P over a ring R is said to be projective if given a diagram of R-module homomor phisms with bottom row exact (i.e. g is surjective), there exists an R-module P → A such that the following diagram commutes (ie, g。h homomorphism h: (a) Suppose that P is a projective R-module. Show that every short exact sequence 0 → ABP -0 is split exact (and hence B A P). (b) Prove...
help with these two
Question 2 Let P(x) = 2x} + 7x2 – 8x +5. Use synthetic division to find the value P(10). O 5,250 O 2,625 O none of these O 2,624 2,626 Question 9 Let f(x)=x2+x, g(x)=x2-1. Find (f+g)(x). o (f+g)(x) = 0 O None of these o (+g)(x)= x+1 of+g)(x) = x4 +x3 - x2-x o(+g)(x)=2x2+x-1 X O (f+g)(x)= X-1
these two please
Question 2 Let P(x) = 2x + 7x2 – 8x +5. Use synthetic division to find the value P(10). O 5,250 O 2,625 O none of these O 2,624 O 2,626 Question 9 Let f'(x)=x2+x, g(x)=x2-1 Find (f+g)(x). off+g)(x) = 0 None of these o+g)(x) = x+1 Of+g)(x)=x4+x3 - x2-x o(+g)(x) = 2x2+x-1 Ov+gXx) = -1