Find the stable vector of r-[}| [ .538 .462 II

Q: prove thats. u.w V.W V.

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Q: 1. Suppose that x is a non-zero vector in a normed vector space V over F, and that a > 0. Find a…

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Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.

A: It is given that

Q: The linearization at a = 0 to v8 + 5x is A+ Bx. Compute A and B. A = B = ||

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Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: In order for vectors and t- 3 in a vector space R3 to be linearly t+4 in depen den t what should t…

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Q: Let S = {A2«2| trace(A) = 0}, i.e. S = Show that -a S is a vector space.

A: The solution is given as

Q: Is it possible to make Z into a vector space if we redefine addition?

A: To check: the possibility to make ℤ into a vector space.

Q: Letr(t) = (t2, 1- t,4t).Calculatethederivativeofr(t) • a(t)att = 2, assumingthata(2) = (1,3,3)…

A: Given that, rt=t2, 1-t, 4t a2=1, 3, 3a'2=-1, 4, 1 Need to evaluate derivative of rt.at

Q: 5. Find a vector æ € R³ such that ||Ax – || is minimal, where [1 1 -2] 1 and b:= 2 1 1

A: By least square approximation ,      To minimize Ax-b the vector x is given by,…

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Q: Q.1 a- Verify Euler's theorem U= x"In(?)

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Q: Suppose that 7(t) is a vector-valued function. Prove that (7 · (7'x7")) = (T'x ") dt

A: We will proof the required result.

Q: The linearization at a = 0 to /3 + 9x is A + Bx. Compute A and B. A = B =

A: Given: f(x)=3+9x

Q: Prove that r(z) = (In-)²-'dt , Re(z) > 0.

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Q: EXercise: Fined the marimal and global Soluation on IR of the Rellowing ODE

A: Given: |t| x'+x=t2

Q: Find the domain of the vector-valued function. r(1) =In(1– 1)i+v4-1j O (-1,4] O 14,-1] O 1,4) O…

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Q: I independent, and that o+zz-5 = 7. Based on the provided information, answe owing questions: ind…

A: Since the question has multiple sub parts we will solve the first three sub parts. Please resend the…

Q: a) T: M, → R, where M, is the vector space of n by n matrices over a field, and T (A) = det(A).

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Q: Find the boundary of the sequence xn in the normalized vector space C [a, b], if it exists. 4 cos 3…

A: The given sequence is: xnt=4cosn3t5+cosnt a=-5π, b=-4π

Q: Suppose that 7 (t) is a vector-valued function. Prove that d (7 · (7'x 7")) = : (7' x 7") dt

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Q: (a) Determine whether the field F(r, y, 2) = (-2, 2, -2az - 62) is conservative or not.

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

Q: is R* is contractible?

A: This is a problem of Topology.

Q: Let there be the random vector Z E Rm Prove that E (||Z||*) = tr(E[ZZ"]) From the expression above,…

A: The answer is in step 2.

Q: Show that the functions e*, cos x, and sin x are linearly independent using the Wronskian.

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Q: Use the least squares method to fit a curve f(x)=ax² + b TO THE POINTS EMPIRICAL (0,1.1), (1,1.7),…

A: Given the points empirical  (0,1.1),  (1, 1.7),  (2, 5.2) We need to fit a curve fx=ax2+b using…

Q: Recall that we say that a random variable X is in the vector space L^2 if it has finite second…

A: Properties of a norm:In order to prove that ||X||2 = √E(X2) is a norm, it must satisfy 3…

Q: 4- Derive the least square equations for fitting a curve of the type b y = a x² += To a set of n…

A: From the given information. The least squares equation is as follows. The x y data is as follows.

Q: 4. Evaluate the Kullback-Leibler divergence between two Gaussians p(x) = N(xu, E) and %3D q(x) =…

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Q: Let Sn=Vn. Find an and show that an O but that Sn=ER=1@k diverges. ->

A: Solution:-

Q: Evaluate the integral.

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Q: The vector F = -ar + 2a expressed in RCS and in terms of is O None of the choices O - = (−cos0sind…

A: We can solve this using spherical co-ordinate matrix

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: prove that T= S.

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Q: Which of these best describes T?

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Q: Which of the following DEs are first order linear DEs?

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Q: Calculate A and B so that t B %3D 1+1 (1-z²)

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Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

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Q: R. find he Corficient of

A: We need to find coeffiient.

Q: 5. Is the vector field F(x, y, z) = (x(z² – y²), y(x² – z²), z(y² – x²)) incompressible? Justify…

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Q: Determine Z- Trans furm in cludig vegiva of con vergence in n 7o メ(At n<o

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Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x + 1/x, a = 1

A: Given fx=x+1x

Q: 1. Obtain the weak formulation for the following BVP: in Ω, -V (kVu) = f u =g on ô0.

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Q: 1 The natural domain of the vector-valued function 7 (t)= In(In is O (-3, 3) O (1, 3) O R O (0, 3)…

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Q: be a normalize s in general for x | ≤||x|*||y|| e or disprove it eans multiplicati

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Q: on vectors for t2 0.

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Q: Consider the vectors x"(t) =( t and x (t) = ( 4t 6. (a) Compute the Wronskian of x) and x2). (1) W =…

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Q: Evaluate t* In t dt

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Q: Determine whether the following are linear operatorson Rn×n. L (A) = A − AT

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