Prove that if A e Mpxn(C) is diagonalizable and either L = 1, or rank(L) < n. L = lim A" exists, then

Q: Find the absolute maximum and minimum values of the function on D, where D is the enclosed…

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Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x3 - 2x + 3, a = 2

A: We find f(x) and f'(x) at x=2

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: 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: Find the linearization L(x) at x= a. f(x) = x+ a = - 1

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Q: Let fn E D[0, 1]. Suppose that fh g on [0, 1], and lim fn(1/2) exists. For each x E [0, 1], show…

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Q: If la,} and {b„} are divergent then {a, + b,} is divergent. True False

A: Given: an and bn are divergent . The objective is to state whether an+bn is divergent is true or…

Q: Consider the Cauchy Problem y 0 = a(x) arctan y, y(0) = 1, where a(x) is a continuous function…

A: We have the given Cauchy problem is y'=a(x)tan-1y,  y(0)=1   …..(1) where a(x) is a continuous…

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: In Exercises 23–30, find Tn centered at x = a for all n. 26. f (x) = e", a =-2

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Q: Show f(x) = e and g(x) = xe linearly independent by finding its Wronskian.

A: Given: fx=exgx=xex The formula to obtain the Wronskian is Wx=f(x)g(x)f'(x)g'(x), where f(x) and g(x)…

Q: please solve this linear algebra problem.

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Q: 3. Show that every y E lị defines a continuous linear functional on l through the inner product,…

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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:

Q: find the linearization at x = a. f (x) = x4, a = 1

A: Given function: Using the formula of linearization of a function f(x) at x =a :

Q: d x"J,(x)=-x"Jns(x) d, n+1 X.

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Q: Show that if A is invertible and DA = CA, then D = C.

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

Q: Show f(x) = e2= and g(x) = x e²z linearly independent by finding its Wronskian.

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Q: Find the d. c. of from definition.

A: Introduction :

Q: 3. Let C[0, 1] be equipped with the inner product (f. g) = f(x)g(x)dx, where f = f(x) and g = g(x).…

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Q: Determine Taylor's formula of order 1 and center a = (0, 0) of f(x)=ex1sin(x2).

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Q: defined BCX,x). a norm Dn

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Q: Looking Ahead Use the Wronskian to show that {e' , te' I is linearly independent on R.

A: Consider the equation

Q: fx) =x+x, aニー Lcx) = ? (メフフ %3D

A: Given that fx=x+1x,      a=−1

Q: (ii) Verify Cauchy-Goursat theorem for f(z) = 5 sin 2z if C is the square with vertices at 1土も-1土。

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Q: Show that if, in using the Laplace development, you accidentally multiply the elements of one row by…

A: A 3×3 matrix a11a12a13a21a22a23a31a32a33.

Q: A function f(x,y) is homogeneous of degree 7 in x and y if and only if, __________.

A: Given problem is solved below.

Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: Prove that for all values of the constant A, eAInt = e In.

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Q: Express the limit lim E (4 cos (272;) + 6)A¤; [2, 4] over as an integral. n- 00 i=1

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Q: prove that E be an elliptic curve over j(E) = 0

A: Given: To prove that the given elliptic curve E over the field Fp2 . And Fp2 is a supersingular or…

Q: (a) It, for f: AC R + R, at Xo, Ak > 0 for k odd, or Ag < 0 for k even, then show that f cannot have…

A: Local minimum is also known as relative minimum. A function f has local minimum at a  particular…

Q: Find the maximum modulus of the function f(z) = -iz + i, |z| < 5.

A: Find the maximum modulus of the functionfz=-iz+iz≤5

Q: prove that the Lollowing examples satisly Laplace eqadion are -2y Cos 2X

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Q: fx) =x+x, aニー %3D LCx) = ? %3D

A: Our objective is to find the linearization L(x) at x=a.

Q: 2n Jnsi (x) = " J,(x) – J(4)

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

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Q: Let {yk } be the DFT of {x; }, where x = [0, –1, 0, 1] y3 = O i -1 -i 1

A: Here, x0=0, x1=−1, x2=0 and x3=1 We have to find y3 Now, y3 is given by…

Q: Find the Runet'ion FCA] such that =t+ cost and such that

A: Let y"(t)=d2ydt2=t+cos t and y(0) = 1 and y'(0) = 2 Integrating on both sides, ∫y"(t)dt=∫t+cos t dt…

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 linearization L(x) of ƒ(x) at x = a. ƒ(x) = x + 1/x, a = 1

A: Given fx=x+1x

Q: Find the angle between x and x4 in C[0,1] with its standard inner product.

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Q: Let M, = Z, – Z;-1, Zo = 0, where {Zn, n21} is a martingale. Show that E(M,„Z„-1] = 0

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Q: Show that e", sin x, cos a are linearly independent using Wronskian Method.

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Q: Find the divergence of the field F. F = yj-xk (y2, x2 1/2 x2- y2 (y2+ x23/2 -x2 ( 2+ x33/2 x2…

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Q: find the linearization at x = a. y = e√x , a = 1

A: Given function: Using the formula of linearization:

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

A: ANSWER:

Q: 1. Find the linearization of r – z at a = 2.

A: Find the linearization of x3-x at a=2.