14. (T/F) Given S = {b.....bx) in R", each p in aff S has a unique represcntation as an affine combination of bi.....bg-

Q: Consider the following inner product R?. on ((T1. Yı), (T2. Y2)) = ax122 + by,Y2 If ||(1, 3)||² =…

A: We will find out the required value of a+b.

Q: get an 6Usc Thesrmn to show that -x gra) = 2 has a unique haed %3D point on

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: If A = x a, – zy a,, evaluate § A · dī around the path L defined by 0 < x < 2,0 < y < 1 as shown in…

A: Stroke's theorem:         It is also known as Generalized stroke's theorem. It states that the…

Q: If the Wronskian of f and g is t cos t - sin t, and if u = f + 3g, v= fg, find the Wronskian of u…

A: It is provided that the Wronskian of f and g is tcost-sint. We need to determine the Wronskian of u,…

Q: Consider the elliptic curve y =x³ – 13x+5 mod 31. Compute the order of the points (10,10) and (7,28)…

A: Form a table of the points and then count the number of points. The total number of points on table…

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: 2.2 Find upper bound of 2+4 (z - 3i)3 +1 where C is the circle |2 – 3i| = 4.

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Q: If Z= cos20+isin 20 prove that = sec² 0 %3D (Z +1)

A: We have to prove L.H.S = R.H.S

Q: Graph the limaçon. Limaçons with an inner loop r = 1/2 + cos u

A: To graph r=12+cosu

Q: Find the reductión Bormula Bor d x In (a+bshmx)"

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Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

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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: Prove that if Y:nz+P(x- mz) So thdz

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Q: Blank 1 is movement of a side of a preimage parallel to that side with respect to one other fixed…

A: We have to fill the blanks.

Q: for the Me quaton of the tagant bie kr the when al Curve

A: We use the definition of the equation of tangent line to the curve y= f(x), at point   (x0 , y0 ) to…

Q: Let C be the shortest path that connects z to ri and /= J, (sinhz + 1)dz. Then O 1 cosh r+ n(1+) O…

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Q: 4. In the diagram below, Ĝl is parallel to NT, and IN intersects GT at A. Prove: AGIA~ATNA

A: Given :GI is parallel to NT

Q: defined BCX,x). a norm Dn

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Q: 9- Show that H= {0 E S6=(6)o = 6} is %3D subgeoup of and find its wight cosets S6 ets left Casets ·…

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Q: Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of…

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Q: See picture below.

A: Consider a function f(x) such that:

Q: Find to the the equation du green funclion corresponding pula)=fex) conditions U(o) =0 with and…

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Q: (b) Compute r if: arctan r + arctan 1 = 2 ( arctan z arctan

A: tan-1x+tan-11=2tan-1x-tan-113

Q: Solve the loieal Vahue Pr blem by the characteristic Hethod Using For a) flx)> 1 and A fx)- K.

A: Solve intial value problem Solving by characteristics equation

Q: 2.2 Find upper bound of 2+4 (z – 3i)³ + 1 where C is the circle |z – 3i| = 4.

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Q: 3. Use Green's Theorem to evaluate G³ï+xj)•dr around the perimeter of the rectangle 0<x<2,0<y<3.…

A: Given ∫C(y2i+xj).dr We know that dr = dxi+dyj Thus ∫C(y2i+xj).dr = ∫C(y2i+xj).(dxi+dyj)  =…

Q: Consider a dihedral groop Dy=<agb: asb= (abj=1 Ds cuss all Dy and verify Subgooups of "Dy=…

A: See answer below.

Q: Graph the limaçon. Limaçons with an inner loop r = 1/2 + sin u

A: Graph the limacon: r=12+sin u. Construct the table of values: u r=12+sin u u=0 r=12+sin 0=12…

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: Q2. In the circle Izl = 1, Find the upper bound for 1924+327+2

A: pleas see the next step for solution

Q: P(5,3) Sinh (폼+북) x +1oydy (6xdx +10ydy 5 C0,0)

A: To show: The line integral is independent of the path. Given integral:…

Q: 3 If C is a circle of radius r with centre z, in the complex z-plane and if n is a non-zero integer…

A: Consider the given integral as, ∮dzz-z0n+1

Q: 12) Show that D- ldi-dal between is shortest distance a x+ by + e2 of i ancd ax +by +Cz = dz?

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Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

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Q: Qsit Prove that the Centre of a gp îs noymal. of

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Q: - Pcosø prove that dw xy is Cont s Lony) - the fun ction (-1, 2) = x*y+z and x = PSinf cse y=pSi- -…

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Q: Evaluate I = Se(sin æ + 7y) dæ + (3x + y) dy for the nonclosed path ABCD in the figure. А 3 (0,0),…

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Q: 12. What is the resulting image of L' after a reflection about the y-axis? Rule: K IN

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Q: 2 Draw the projection of b onto a and also compute it from p=za: |3D COs O sin 0 (a) b = and %3D a =…

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Q: Consider the following PDE Uxx + 2x uxy + Uy = 0 a) What is the class of the equation? b) Reduce the…

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Q: Find the absolite marima and minima points between [o,u] gf y : * + 2dx' sunchion is porsbl.

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Q: => For The Wbech Ualuo of E doas the Martrix イK %3D have one roal eaomalue of Mutiplicty?? k =

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Q: Verify that cos kx a solulion of Also, stafe what kind of DE is the DE above

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

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

Q: 2.2 Find upper bound of zp (z- 3i)3 + 1 where C is the circle |z - 3i = 4. 2.3 Use the Cauchy…

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Q: In C[0, 27], with the inner product -2 (f, 8) = | f(x)g(x) dx, show that the set S = {1, sin x, cos…

A: Given: Inner product defined as: &lt;f,g&gt; = ∫02πf(x)g(x)dx To show that the set S = { 1, sinx,…

Q: 3.1 Show that upper bound of fe dz, where C is the circle |z + 4 – il = 7. z+5i-1

A: The given problem is to find the upper bound of the given complex integral over the region of circle

Q: Find the domain corresponding to the inner loop of r=1+2cos(theta)

A: The domain  inner loop of r=1+2cos(θ)  is 0,1