If e-ispure imaginary W hat Restriction is placed on z?

Q: 8.0. If x-(x,, X, ...,%)«R', define [xL by Prove that xJkL is a norm on R'. N I|} dns - x]

A: We will solve the first question highlighted in yellow. If you want the second question to be…

Q: Are x, sin(x) and cox(x) linearly independent

A: True x, sin(x), cos(x) are linearly independent

Q: -Use Cauchy- Riemman eauadiane to shaw that euch of there tiers is entire. a fizlasxy ti(zy-x) b.…

A: Note: we answer up-to 3 multiple subparts. Please resubmit question which you would like to get…

Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

A:

Q: - Show that the norm tion t= aT+B. Use [a, b] onto [0, 1] (7) = 1, ý(7)= T, V т,

A:

Q: Let E={(r,0,z) : os es T, OS zs 1, 5Vzs rs 5. Compute

A: Introduction: The triple integral ∫∫∫Ef(x,y,z)dV with the region E=(x,y,z):a≤x≤b, c≤y≤d, e≤z≤f can…

Q: Consider X = C[0, 1] with the norm = max |x(1)|, IE[0,1] and let T: X - X be the mapping given by…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: of all Z € C that z iz e = e a Descnibe and sketch the set

A:

Q: Show that a set {V1, ..., Vp} in R" is affinely dependent when p > n + 2.

A:

Q: If E and E, are measurable , then (E,UE,) is not measurable. ylgn

A: False.

Q: 2/Define the topology If X-R² and T = {GK, KERZULAR} GK = {(XY) ER²|x+y >K3 Prove is topolgy on R²

A:

Q: Show that if A is closed in X and B is closed in Y then A × B is closed in X × Y

A:

Q: The Wronskian of y,(t)=e 2, y,()=e" is-e St. Select one: True False

A:

Q: Let E Os 0s n, 0s zs 1, 8Vzs rS 8. Compute

A:

Q: If there exists open ball B (a, r) such that B (a, r) nG=Ø then a is not limit point of G

A: To check whether there exists open ball B(a, r) such that B(a, r) ∩ G= ∅, then whether a is not…

Q: If E, and E2 are measurable , then (E,UE,) is not measurable . صواب İhi

A: Here we have given E1 and E2 are measurable sets

Q: Let (X, T) be a topological space, AcX, then A'next (A) = 10 AO

A:

Q: c If in is an involution of X, show that (r, y)in = (yi", rin) is an involution of X12). %3D

A: Given X is a lattice. Given in  is an involution of X To show: x,yin=yin,xin is an involution of X2…

Q: Show that R³ is spanned by S = {(1,1,1), (1, –1, 0), (0, 1, – 1)}.

A:

Q: The set S=[1,3) is not compact. Which open cover of S contains a finite subcover?

A: This is the question of Topology.

Q: Let A, B, and C e M,(C) such that ВС - СВ %3D А"А prove that BC = CB.

A:

Q: 2. Show that the set 3 S = 3 2 2 2 2 spans all of R³ or find an element of R' not belonging to…

A:

Q: Show that R³ is spanned by S = {(1,1,1), (1, – 1, 0), (0, 1, – 1)}.

A:

Q: Let T={[a, ) : a€R}, then T is not Borel algebra.

A:

Q: Find a norm for C([0, 1]), so that C([0, 1]) is not complete under this norm.

A:

Q: If e ispure imaginary What Restriction is placed on z ?

A:

Q: Let T={[a,0) : aER}, then T is not Borel algebra

A: Given a statement

Q: Prove: If U is a neighborhood of x0 and U ⊂ V, then V is a neighborhood of x0. Also, if U1 ..., Un…

A: The neighborhood of a point: Let (X, T) be a topological space and x0∈X. A neighborhood of x0 at is…

Q: Prove that the Joukowski map 1 p(2) : (z + maps ONTO T - (-1, 1)

A:

Q: If z, w E C, prove that z+w=z+w.

A: This follows from simple substitution. The detailed solution is presented in step 2. As requested i…

Q: Prove that if a, b E Z - {0}, then gcd(a, b) = gcd(a, -b)

A: soln:gcda,b=Greatest common divisor of a and bEvery integer that divides a and bsimultaneously will…

Q: 1. Let T and S be topologies in X. Show that SnT is also a topology in X.

A: 1.

Q: Is ZXZ cyclic? [Here Z means (Z, +).]

A:

Q: Prove using Venn diagram that An (B U C) = (A n B) U (A n C)

A:

Q: A chow that the wsonskian d es will neves become zex0 to8 all spal

A: Here we use the fact ex> 0 ,for all real x.

Q: prove that Sa/Gn has f discription with M-ly ny-l Degrees tof freedom

A: Suppose that xi and yi are two random samples of size n, drawn from a normal population.  Population…

Q: In general, for a a) S is compact 2) Sis closed at S is compact

A: We use definition of compact metric space, totally bounded set, Closed set, accumulation point or…

Q: Let J={(a, ∞ ) : a€R}, then T is Borel algebra. ulgn O

A: Given a statement

Q: let FC k be a Galois extension with Gal

A:

Q: Let the non-empty set S = {x - yv3:x,y ER}, show that S is closed'under multiplication then find the…

A: We have to show that the given set S=x-y3:x,y∈R is closed under multiplication and also find the…

Q: 3. Show that a reflection a in the x-axis defined by o(x, y) = (x, -y) is an isometry.

A: The solution of given problem is followed by

Q: 2

A:

Q: Show that R3 is spanned by S = {(1,1,1), (1, –1,0), (0, 1, – 1)}

A:

Q: If E and E, are measurable , then (E,UE) is not measurable

A: False.

Q: Let X = {a, b, c, d, e} and let T ={X, Ø, {a}, {c,d}, {a,c,d), {b,c,d,e}), therm %3D O (X,T) is…

A:

Q: Let A = {x E Z* : x is a mutiple of 2 and x < 15}. Rewrite A in roster notatlon.

A: Given that : A = {x∈Z+ : x is a multiple of 2 and x &lt;15 }   Roster form : A representation of a…

Q: Suppose that A = SS−1, where  is a diagonalmatrix with diagonal elements λ1, λ2, . . . , λn. Show…

A: