2.11 D.ll Let cRidul be amet (ic Then the falwing ard space are equivalent @ P is continuong onX (a (e) CLf cB)Ÿ for all sulbset of B @fCA) c fCA') for all subsed A af X

Q: Let z= y- 4a, a u'v and y-v- 3u. Compute On kum)-(1,1) -

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Q: 18/156) If the Wronskian W of f and g is te' and if (t) = t, find g(t) %3D

A: Given that gx, y=t2et with ft=tTo find gt

Q: 6) Suppose V is a finite-dimensional with dim V > 1 and T e L(V). Prove that {p(T)lp € F[x]} # L(V).…

A: The complete solutions are given below

Q: 3. Let SP(la, b, c,d.e) and define W:SXSS as the union function: (A, B)AUB. for ill (A. B) ESXS. (a)…

A: Given: S=P({a, b, c, d, e})Define A:S×S→Ssuch thatA(A, B)=A∪Bfor all (A, B)∈S×S We see that S is a…

Q: a) Assume that y is a continously functian in t. Evaluate differ entiable TT to

A: Given ∫xexπyty'tdt

Q: c) For x e ll n2, define || x ]| = || x || 1+ || x ||2: Show that (11 n2, ||· || is a Banach space.

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Q: 02 Define a Map L: M232M.3 by 1 3. LHA)-1 A, Is L a L2 lincar transformotion? Pove yovy AssertionB

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

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Q: 2. Find all volves of tand u x(t,4)=0 and simultomebusly such that =0. 3. 5x-11* C.

A: Get the equations for:  fx=0fy=0 15x2-11y=0-11x+3y2=0 or 15x2=11y3y2=11x

Q: of discon tinuity of the the following func Hions (a) g(x,y) = stuind %3D (b) b) f laiy)

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Q: 5. Prove that the baker map 2x B(z) = 2z - 1 <z<1 is chaotic on (0,1).

A: Given the baker map, Bx=2x,0≤x≤122x-1,12≤x≤1

Q: let H = {n² |n E z*}, determine whether it is closed under

A: Given : H={n2|n∈Z+}   To Check:  H is closed under binary addition or not

Q: 2) Determine the dimension of Null A and Col A for the marix 1 2 30 0] A =0 0 1 0 1 0 0 0 1 0

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Q: Find yas a fon chenof x if t. %3D with

A: This is cauchy euler equation and we will solve it by changing the dependent variable

Q: let H = {n² |n e Z*}, determine whether it is closed under

A: Here, we have H=n2| n∈ℤ+. To show the set is closed under binary multiplication. This means we have…

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: Suppose N E L(C) is nilpotent and has a Jordan form with only one Jordan block. Describe a Jordan…

A: According to the given information,

Q: -1/2 8. Ž Pn (x) q^ generobr x,2) = (1-2xz + 2?) of legendre polynañials ,oblin the (2n+) xPa W=h+D…

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Q: 3. Find all the fixed points and classify cach of them: f(r,u) ryev,

A: Solution:- Fx,y=xye-x2-y2 Put Fx=0 and Fy=0 Fx=e-x2-y2y-2x2=0and Fy=y-2y2 e-x2-y2=0 So,  0,0,12,12,…

Q: Et: let A = 13-202 07 2 6-5 -2 4 -3 5. 26084 18 Find a bosis Por 5 10 o 15 Phe null space of

A: Answer is mentioned below

Q: 6.1 let T be a l'iner transformatio from Mga into M,a Sub that %3D

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Q: 4:x→X (when X is a normed Space) is continous at xo € X iff for any Sequeue ie AS n s

A: Let f:x→X (when X is a normed space) is continuous at x0 ∈X iff for any sequence  xn ∈X, xn→х0  ⇒…

Q: 4) Osig the inteecal de finiton, find the convo wto a gis diaM fug a of f(+)= cs 2+ 9C-) = e b)…

A: Given:

Q: 2.2.15. Let X be a metric space, and suppose that xn → I and yn → K. Prove that d(xn, Yn) – + y in…

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Q: 6. Consider the horizonal strip 2 = {z+ iy : -1 < y < 1}. There exists a holomorphic function f on…

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Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: 8. let C be the curue space ret) = (e*,2et ,2et ),0s ts lnca) the rength of C is

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Q: 2) Determine the dimension of Null A and Col A for the marix [1 2 3 0 0 A =|0 0 1 0 1 0 0 0 1 0

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Q: metoix space and d[211?(₂) for all ₁2 ER 2,12₂ 17. (*/ 1²(₂) d is matrie X. let (Xid) be d' XXR…

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Q: The area bounded by the curve y = 7x and the lines z= 2 and =9 above the z-aris is O 539.00 square…

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Q: (2) Show that if dim(V) = k (so in particular, T has k distinct cigenvalues), then there exists v e…

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Q: (b) Consider X = C[0, 1] with the norm %3D = max |x(1)), re[0,1] and let T: X X be the mapping given…

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Q: 1. Let TE L(V) and suppose v is in the range of T and w is in the null space of T". Show explicitly…

A: To solve we will use the definition of adjoint operator.

Q: #Let Vz arih Here, れgl。 and hahe what netationship must hold betaen adho foro v to be ewoatly…

A: The expression for the volume is V=πr2h.   Thus, the total differential is given by dV=∂V∂rdr…

Q: Question # 01. Consder z= {acbos a-b =0; S2 Interpet that eguivale nce relation. ~ 18 is

A: That's easy, just show that this relation is reflexive, symmetric and transitive.

Q: a sondom Semple XSI .Detemie a clistrbutian with Size n Conider (df F(m) =1 -x² Sei juences has…

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Q: let a-Rbe ametric sPacesConsir he following subsed ofP @ Show that Dra De are comPact Setsornot of D…

A: Question from real analysis.

Q: Which of the following is a nonlinear second order nonhomogenous PDE a. xux-Uxx=tuxt O b.…

A: To find - Which of the following is a nonlinear second order non-homogenous PDE x ux - uxx = t uxt…

Q: Suppose S is the unit cube in the first octant of uvw-space withone vertex at the origin. What is…

A:

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

A: Here we use the fact ex&gt; 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: find the desivalive d the functian ha)= ainfse and compute h'(2) Th o

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Q: 1 : Determine the manimom and Nalve of the function minimumn x'tyス condition under the *+ 2 7?== 1.

A: To find the absolute maximum and minimum of the function using lagrange multiplier

Q: If F G) and g(x) are conbinuous on [anb] andit =Sprove thab. SF= 58 prove thab Icefanb] Such that…

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Q: consider the map given by F(x)=1-x² discuss the charactristics of the orbits starting at x=0

A: As per the question we are given the following map : F(x) = 1 - x2 And we have to explain the…

Q: Let fons =loag, Cln). Find t'ot at

A: Given, f(x)=logx(ln(x))

Q: 2 - Find the inter val on which f are Con Cave down and infleobion Points a -y = x2 5X+10 6- ソ= (¥+…

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Q: Show that if AT Ay = y for all y in Rn, then AT A = In.

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Q: me with action space A = (a1, az) and parameter space e = {0, 02} has the following loss ma %3D P2…

A: Here the action space i A={a1,a2}