The linear operator T: R2 --> R2  defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?

Q: Find the linearization of the function at the given point. f(x,y z) = 3xy +4yz +3zx at (1,1,1) O A.…

A: We have to find the linearisation functions

Q: Linear operator T: R2 R2 is defined by T(1,0) (1,4), T(1,1)-(2,2) T one-to-one?

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Q: Find the linearization of ƒ(x, y) = x2 - xy + 1/2 y2 + 3 at the point (3, 2).

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Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: Find the linearization of ƒ(x) = 2/(1 - x) + √(1 + x) - 3.1 at x = 0.

A: Here The formula for the linearization is Here a = 0 Therefore,

Q: Use the chain rule to evaluate fu and f, at (u,v)=(2,-2) where f(x,y,z)=y³+xz² and x=x(u,v)=u+v²,…

A: Concept: The chain rule for the function f (x,y,z) is  dfdu=∂f∂x∂x∂u+∂f∂y∂y∂u+∂f∂z∂z∂u…

Q: please solve this linear algebra problem.

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Q: Consider the linear operator defined by Show that T is compact. E1 E2 E3 T:l² l², x = (1, 2, 3, ...)…

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Q: Find the orthogonal trajectories of x = C exp (-y²). Oy=C*exp(-x) Oy=C*exp(2x) Oy=C*exp(-x^2) O…

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Q: Find the linearization of f(r, y, z) = x + y² + z³ at the point (1, 2, -1).

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Q: Find the linearization L(x, y) of the function f(x, y) = V161 – læ2 – 16y² at (-4, –3). L(x, y) = ||…

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Q: 2x+ 3y-z =1 4x + y-3z = 11 3x-2y +5z = 21 | %3D

A: Solution:

Q: Find the Linearization L(x) of y = (1+x)¬1/² at a = 8. L(x) = %3D

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Q: Q1) Use a suitable Linearization to find the best fit of the form f(x) = Cx3 + for the %3D data:…

A: Given the data,                 (1, -1), (2, 7), (3, 26.3)

Q: The local linear approximation of (1- x)2° at x, = 0 is a) 20 - x c) 20 +x b) 1- 20x d) 1+ 20x

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: The linearization at a = 0 to v4 + 4x is A + Bx. Compute A and B. A = B = %3D II

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Q: 25. Suppose that T: R2 → R² is a linear operator such that T. -1 | T. -1 Is it possible to determine…

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Q: fx) =x+x, aニー Lcx) = ? (メフフ %3D

A: Given that fx=x+1x,      a=−1

Q: Maximize the function f(x, y, z) = x² – y², given that x² + 2y² + 3z² = 1. %3D

A: Here, we can use Lagrange multiplier to maximize f(x,y,z)=x2-y2 with constraint x2+2y2+3z2=1. Let…

Q: Find the linearization L(x) at x = a. 1 f(x) = - x - a = 1 %3D -

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Q: Find the orthogonal trajectories of x = C exp (-y²). Oy=C*exp(-x) Oy=C*exp(2x) Oy=C*exp(-x^2)…

A: Given problem:- Find the orthogonal trajectories of x = C exp (-y²).

Q: find the linearization at x = a. y = (1 + x)^−1/2, a = 0

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Q: Verify, if u = x + y+ z, v = x° + y° + z³ – 3ryz, w = x²+y² + z? – xy – yz – za are functionally…

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Q: Find the linearization L(æ) of y = (81+ 2æ²)-1/2 at a = 0. L(x) =|

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Q: Ques. 3: Check whether the operator T: R2 → R² defined by T(x,y) = (y,x) is linear. Moreover if T is…

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Q: (b) Show that the Linear guen Operators. are not with T(f)= Lf6), f()+1].

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Q: let f (x, y) = x² + xy + y². Using the chain rule, calculate %3D af -(u(x, y), v(x, y)) being u = v…

A: Given that                                   f(x, y)=x2+xy+y2 And also we have…

Q: Determine the Linearity of this DE. * y" -xy' + y =D0 O Linear O Non-Linear

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Q: find the linearization at x = a. y = (1 + x2)^−1/2, a = 0

A: We find the derivative of the given function using power rule and chain rule

Q: Exercise 4.12 Give an cxample where f(x) - b as x → a and g(y) + c as y – b but g(f(x)) + c as x → a

A: To find an example where fx→b as x→a and gy→c as y→b but gfx→c as x→a. Let b∈ℝ be a fixed real…

Q: s the linear operator T : R3 --> R3 defined by T (x, y, z) = (2x - 3y + 7z, 5y + z, -z)…

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Q: 3. Find an admissible extremal for the problem of minimizing J[a] {Gi² + xi + x + à} dt with x(0) 1…

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Q: Find the linearization of ƒ(x) = 2/(1 - x) + saqrt(1 + x) - 3.1 at x = 0

A: Given,

Q: Let, T: R3 → R³;T(x, y, z) = (2x + y, y – z,2y + 4z) Find the rank and nullity of T.

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Q: Find the orthogonal trajectories of the family of lines 3x + 5y = C (A 3x - 5y = k (B 5x + Зу - k ©…

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Q: Find the linearization of f(x,y) at the indicated point (Xo,Yo). f(x,y) = /x +2y; (4,7) L(x,y) =

A: Given:- f(x, y) =√x+2y To find:- linearization of f(x,y) at the indicated point (xo.Yo). f(x,y)=√√x…

Q: 19: Find two linear operator T, and T,on V(R) such that T,T, = 0 but T,7, - 0.

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Q: Show that the functions f (x) = |x + 1|and g(x) = x² are linearly %3D independent on the interval I…

A: Given that f(x)=|x+1| So, f(x)=x+1 in [1, ∞) g(x)=x2

Q: The Wronskian has been computed. Determine whether the functions are linearly independent or…

A: Here given the wronskian of function ex and 2ex is zero.

Q: Find the orthogonal trajectories of a system. x'y2- 2xya + a2 0 %3D

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Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

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Q: Let T: R² → R² be the linear operator given by 7 ] - ([ ; ) = [ - {|- } {} } -x + 2y Зх + у and let…

A: We can solve this using given information

Q: Ques. 3: Check whether the operator T: R2 → R2 defined by T(x, y) = (y,x) is linear. Moreover if T…

A: A mapping T:R2→R2 is a linear transformation if and only if a) T(u)+T(v) = T(u+v) b) T(cu) = cT(u)…

Q: show that the L operator is linear for y" – 4y" + 2y' + y = x2

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Q: íf was T'fz (R)→R Linearidentifier grand father ♡ Kert ☺ Im T

A: Here given that a linear identifier T :ℙ2ℝ→ℝ3 defined by Ta+bx+cx2=a, b, a+b. We have to find Ker T…

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…