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Define f: R2R3 b f(s,t) (sin(s) cos(t), sin(s) sin(t), cos(s)). (a) Describe and draw the image of f. (b) Proeve i.baat uts dilikur#xot.ial le. (c) Find the Jacobian matrix of f at (π/3, π/4) (d) Describe and draw the im age of Df(m/3, π/4). (e) Draw the image of Df(n/3, π/4) translated by f(n/3, π/4). (f) Describe the relationship between the image of f and the translated image of Df(T/3,/4) in nart (e Define f: R2R3 b f(s,t) (sin(s) cos(t),...
6. (16 points) Let CE C be a primitive n-th root of unity. Let X = 6 + 1/5. (a) (4 points) Show that Q(5) R = Q(1). (b) (4 points) Let f be the minimal polynomial of over Q. Show that Q(x) is a splitting field of f over Q. (c) (4 points) Show that Gal(Q(^)/Q) – (Z/nZ)* / (-1). (d) (4 points) Find the minimal polynomial of 2 cos(27/9) over Q.
Problem 3. Let V and W be vector spaces of dimensions n and m, respectively, and let T : V -> V be a linear transformation (a) Prove that for every pair of ordered bases B = (Ti,...,T,) of V and C = (Wi, ..., Wm) of W, then exists a unique (B, C)-matrix of T, written A = c[T]g. (b) For each n e N, let Pn be the vector space of polynomials of degree at mostn in the...
4.let U= {q,r,s,t,u,v,w,x,y,z}; A= {q,s,u,w,y};and C={v,w,x,y,z,}; list the members of the indicated set , using set braces A'u B A.{Q,R,S,T,V,X,Y,Z} B.{S,U,W} C.{R,S,T,U,V,W,X,Z} D.{Q,S,T,U,V,W,X,Y}
match numbers 1,2,3,4,5 with the letters - 2 - rt CE - - 18 — 3 4 5 - 21 22 * X/Y 20 ESNO T 21 2 கவா s A B C D E F G H I J K L M N I 21 P Q R S T N V w Х
If S={x | 0<x<12}, M={x | 2<x<6},and N={x | 4<x<12}, find (a) M∪N (b) M∩N (c) (S∩N)′ (d) M′∩N′ a) x | 2 < x <12 b) x | x = 5 c) little confused on d)also confused on, Help please.
QUESTION 2. Suppose that S= {n e Z (Si Z)(n = 7i + 3)}, T= {n E ZI (3j e Z)(n = 7j - 4)}. Prove that S=T.
1. Second order transients Z. Z V (t) Z Z N 2 The switch is in the left position and moves to the right position at t=r where >0. Let Z, be a resistor, R. Z be a inductor, Ly, 2, be a capacitor, Cr, Z. be a resistor, Rp. 2 be a resistor, Rs. Zo be a capacitor, Co, and the input voltage, vy(t) =uſt) volts. This question is about the voltage across the capacitor: Cg. viz., V.(s), v)....
solved item S, T, U, V, W, X, Y, Z The demand for subassembly S is 100 units in week 7. Each unit of S requires 2 units of T and 1 unit of U. Each unit of T requires 1 unit of V, 2 units of W, and 1 unit of X. Finally, each unit of U requires 1 unit of Y and 2 units of Z. One firm manufactures all items. It takes 2 weeks to make S,...
3. Let t be the co-ordinate on A (C) and let z, y be the co-ordinates on A2(C). Let f 4z? + 6xy + x-2y® E C[x, y] and let C be the curve C-V((f)) C A2(C) (You may assume without proof that f is an irreducible polynomial, therefore C is irreducible and I(C)- (f).) (a) Show that yo(t) = (2t3, 2t2 + t) defines a morphism p : A1 (C) → C. [3 marks] (b) Show that (z. У)...