Let T: 1 1 be defined by (1, 62, E3,) (0, 0, 6, E). Is T bounded? Self-adjoint? Positive? Find a square root ofT

Q: Let R = [0, 12] × [0, 12]. Subdivide each side of R into m = n = 3 subintervals, and use the…

A: Given ∫∫4y-x2dA

Q: Find the best-fit quadratic function f(t) = co+ c¡t + czť² to the data points (0, 7), (1, 6), (2,…

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Q: Evaluate f a'y*da + =*ydy counterclockwise around the square with vertices (0,0), (1,0), (1,1), and…

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Q: (b) Let f(t) = (t- 2)*(t +1)² be the characteristic polynomial for a linear operator T. Obtain all…

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Q: Find a norm of the function f(t) = t² in space C" 0, 1, where norm is given by formula max|f(t)|+…

A: Solution

Q: Let f(t) = (t – 2)*(t+1)² be the characteristic polynomial for a linear operator T. Obtain all…

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Q: Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(x) = 0 on [a, c] Show that…

A: Cubic Interpolation Polynomial : Let  for  be the points satisfying the function . The cubic spline…

Q: ® Find the_functian that satisfies the following conditions for some constant Eceficients c,and c…

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Q: Fit a quadratic function of the form f(t) = co + ct + czť² to the data points (0, 0). (1, 12), (2,…

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Q: Q5. Let k > 0. Prove that if t„m <x < tm+1; then m EGB (#) = E «B (z). iEZ i=m-k Here B denotes the…

A: A spline of degree n is a piecewise polynomial function if degree k-1 in a variable x. The spline is…

Q: Define an operator T: fºº → f° by T(5₁) = (¹) # and bounded. for each (₁) E. Show that T is linear…

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Q: Find the absolute maximum and minimum values of f on the set D for f(x, y) = x² + y? – 2x, where D…

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Q: (d) Show that T is bounded and find ||T||. (e) Find the adjoint T* of T.

A: We will use the vector/matrix notations to visualise things easily.

Q: Evaluat..f.x.dA. wha.is.the..sgiem.in.the.fiigt. R quandrant..bounded..xy=16. X..8....y.z.. y.e.x...

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Q: Fit a quadratic function of the form f(t) = o + ct + gt? to the data points (0, -5), (1,0). (2, –1).…

A: Least squares polynomial

Q: Consider P2 with the inner product (p, q) = | p(x)q(x) dx . Let U = span{1,2x + 2} and g(x) = 3x? +…

A: Consider P2 (polynomials of degree atmost 2) with the inner product defined as follows, p, q=∫-11…

Q: Consider P2 with the inner product (p, q) = | | p(x)q(x) dx . Let U = span{1, 2x + 2} and g(x) = 3x2…

A: See the detailed solution below.

Q: find the linearization L(x) of ƒ(x) at x = a.ƒ(x) = sqrt(x2 + 9), a = -4

A: Given function is, fx=x2+9, a=-4.   The objective is to linearize Lx of fx at x=a.   It is known…

Q: Let Ps have the inner product given by evaluation at-2,-1, 0,1, and 2. Let p(t) = t2- 2t and q(t) =…

A: Let P3 have the inner product given by evaluation at -2, -1, 0, 1 and 2 . Let p(t) = t2-2t  and q(t)…

Q: Q.4.(a). Show that the following functions is not an inner product on R3, where u = (u, U2, U3) and…

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Q: Let xj = xo + hj for j = 0, 1, 2. Use the quadratic polynomial interpolating f at those nodes to…

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Q: Let D be the portion of z = 2x + 5y inside x² + y² = 1, oriented up, and let F = (3, 2, -2). Compute…

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Q: Find all valus of z such that (5 + z)6 = (1+ i)z6

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Q: Find the area of a region enclosed by the parabolas f(x) 2 > 12 - 1 for all z in [0, 1]. = T and…

A: Topic = Area

Q: Let A = Z. Let R be defined on A x A where a Ry if 4 (x- y). Prove that R is transitive.

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Q: Define T : R? → R by 7((x, y)) = x+y. Describe the kernel of and fibers of T geometrically.

A: The kernel is a line with slope -1 and passes through the origin.

Q: Let f(x) = + 3x? + 4x. a) What is the kernel of f? b) Compute the minimum and the maximum of f.

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Q: Find a norm of the function f(t) =t – 2t in space L10, 1] 1 a. 6 С. е. d. ai

A: We use the definition of norm in L1[0,1] to answer the given question.

Q: Determine if the veetor is in Spanis} where S-3,01,2,0L3,4,2, 183 Ifit is, write T as a linear…

A: The solution is given as

Q: Find a norm of the function flt)= t+2t in space C^co13 %3D where normis given by formula ms x…

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Q: Let a < c < b and s(x) be a cubic spline with a single node c. Suppose s(x) = 0 on [a, c]. %3D Show…

A: Let a&lt;c&lt;b and sx be a cubic spline with a single node c. Let us consider sx=0…

Q: Please solve

A: Consider the given function.

Q: Let ū = 2i – k and ī = i+3j + k. Compute |ū], |T], ū x ī, and Projzū.

A: Solution is here

Q: əz Let z = x² + y³, x = 2st and y = s-t². Compute for and ar

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Q: Fit a quadratic function of the form f(t) = co + cit + czť² to the data points (0, –6), (1, 2), (2,…

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Q: Let R=[0,6]×[0,6]. Subdivide each side of R into m=n=3 subintervals, and use the Midpoint Rule to…

A: Given :  R=0,6×0,6m=n=3     MIDPOINT RULE:

Q: Suppose (Mt)t>o is a bounded martingale. (a) Show that for 0 < s <t (b) Show that for 0 <a<b< s <t…

A: As per the question we are given a martingale (Mt)t≥0  And we have to prove that : E[Mt2 - Ms2 |…

Q: Let T: R3→ R be linear. Show that there exist scalars a, b, and c such that T(x, y, z) =ax + by + cz…

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Q: Determine the quadature rule of the form | f(r) dr = Aof(ro) + A1f(£1) + - *·+ Anf(Tn) a. when the…

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Q: Find the foo The funetton f(2) zl-Xt +Zte? zeso and its oodes MERA

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Q: Let r; = ro + hj for j = 0,1,2. Use the quadratic polynomial interpolating f at those nodes %3D %3D…

A: The solution is given below

Q: find Fourier sertes [o, 2w] an くxく下 O f cx)= (2 2下-X πく*く 2x fcx) = こ 2.

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Fit a quadratic function of the form f(t) = co + cit + czť² to the data points (0, 1), (1, –7),…

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Q: Fit a quadratic function of the form f(t) = co + Ct + czť to the data points (0,0), (1, 12). (2, 6).…

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Q: Define g : Z → Z × Z by if t is even if t is odd S (t, t + 3) g(t) = I (t, 2) Is g injective? Is g…

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Q: let f(z) = z2 + z find the maximum value of If(z)| on the square A = {z € C:0 < x,y < 2}

A: We have given function fz=z2+z where, z=x+iy complex number We have to find maximum value of fz on…