Let L: R -R be defined by ()- -2 -1 L 3 2 2 1 1. Show that L is invertible. (E) 2. Find L

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A: We have to state true or false.

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Q: 3. Let L be a linear operator on R and let L(1) = a . Show that L(x) = ax for all x E R .

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Q: a) Show that fi (x) = cos x, f2(x) = cos 2x are orthogonal on [-7, n].

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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Q: please solve this linear algebra problem.

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Q: Consider the ARMA(2,1) process (1+0.6L)(1+0.2L)y, = (1+0.5L)e, . (a) Construct an autocorrelation…

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Q: 2. Use Wronskian to show that fi = x, f2 = ln x, and f3 C° (R). x In x are linearly independent in…

A: Concept:

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A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: 1) Find the norm of the following operators d) T:C[0,1] → C[0,1] by (Tx)(t) = f¿(t - s)*x(s)ds

A: Norm of operator gives the idea of size of any linear operator. Norm of can be found as .

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A: Given that, A is invertible and DA=CA.

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A: W need to find elements which are invertible inZ4x,y.

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Q: (a) Let f(r, y) = -2r*y² – In(y²). Compute fyzz (b) Let g(r, y, 2) = 1(3y* – 52²). Compute

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A: See the detailed solution below.

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A: The solution is given as

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A: Let f(z) = z5, show that f is invertible in a neighbourhood of i and calculate(f-1)' f(i)

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Q: Q3: a) Let ƒ : Z → Z be such that f(x) = Vx² – x + 1. If invertible, and if it is, what is its

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Q: Prove that F(z) = 81 8z + 1 is chaotic on (-1,1).

A: To prove: Fx=8x4-8x2+1 is chaotic on -1,1. First plot graph of given function with -1,1 as follows:

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A: Given : B is an n×n complex matrix with  B3 = O , where O is zero matrix. To prove :  I-B is…

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Q: If T: H→→H is a bounded self-adjoint linear operator and T‡0, then T"#0. Prove this (a) for n = 2,…

A: Given T:H→H is a bounded self-adjoint linear operator and T≠0. We know that if T is a self adjoint…

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A: To show that the matrix is invertible.

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A: As it's mentioned in the question to answer between a) or b), so showing steps for only one part. b)…

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Q: In C[-1,1], with the standard inner product f(x)=ex and f(x)=e−x are orthogonal. true or false?

A: true please see explanation in step 2

Q: Q6. Let C[0,1] have the inner product < f,g 2 S,"f(x)g(x)dx and let fn= cos nx (n=0,1,2,3,....).…

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Q: Consider the following operator A : L²[0, 1] → L'[0, 1] A(f)(x) = (f(x))² + f(x). If this a linear…

A: Given, the operator  A : L20, 1→L10, 1 defind by                               A(f)(x)=(f(x))2+f(x)…

Q: 15.If the Wronskian of f and g is t cos t − sin t, and if u = f + 3g, v = f − g, find the Wronskian…

A: Consider the provided information, Wf,g=fg'-gf'⇒tcost-sint ...... (1) Find the Wronskian of u and v.…

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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: 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: If Ø : R3 → R3 be defined as Ø (x,y,z) = (2x, 4x –y,2x+ 3yz) then show that Ø is invertible. %3D

A: Given that ϕ:R3→R3 is defined as ϕx,y,z=2x,4x-y,2x+3yz. Now, ϕ is invertible if ϕ is one-one and…