Let L : R → R² be defined by L(æ) = L T2 (:) - () Show that L is not a linear transformation by finding vectors æ, and , y such that L(æ + y) + L(x) + L(y): æ = (x1, 22) y = (Y1, Y2) Prove your answer by calculating (for your choice of æ, y): L(æ + y) =| and L(æ) + L(y) Note: This problem has infinitely many correct answers.

Q: Suppose T: R-→R2 is a linear transformation. Let U and V be the vectors given below, and suppose…

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Q: Prove or disprove whether the transformations T defined below are linear. (i) T(x1, X2, X3) = (x3 –…

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Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: Consider the data: (zo, f(xo)), (₁, f(x1)), (2, f(x₂)), (#3, f(#3))).\\ The Lagrange basis…

A: Lix=x-x0x-x1·..x-xi-1x-xi+1·...x-xnxi-x0xi-x1·..xi-xi-1xi-xi+1·...xi-xn∴Lixj=0     for i≠j1     for…

Q: [x + y-z] 2хy Lx + z +1] 2. Determine whether the function T: R3 →R3 by T is a linear transformation…

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Q: Let V₁, V2, and V3 be vector spaces and T₁ : V₁ → V₂ and T2 : V2 → V3 be linear transforma- tions.…

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Q: Q1. Let u= (1, 1), addition and scalar multiplication on Vas; u+v=(₁+y₁-1, 2+2-1) and a.u = (ay,…

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Q: Let P, denote the vector space of polynomials in the variable of degree n or less with real…

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Q: [2х — у 1. () = [x + 3y] Determine whether the function T: R² →R? by T is a linear transformation.

A: Use definition of linear transformations and two step test of linear transformations.

Q: Let y = proj₁y = 3 -2 and u = -3 (a) Find the orthogonal projection of y onto u. 2 1 = (b) Compute…

A: Here we have to find orthogonal projection of y onto u and also we have to calculate distance d.

Q: Let P, denote the vector space of polynomials in the variable of degree or less with real…

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Q: THEOREM 4.4 (LINEAR TRANSLATION) Let Y= aX + b; then: My(0) = eb" My(a0).

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Q: 4. Given two bases (b) = transformation y : R² → R² with respect to the basis (f) and let X, be a…

A: Given two bases b=b1,b2 and f=f1,f2 of ℝ2  where  b1=12, b2=34, f1=11, f2=23 Let Af be a matrix of a…

Q: 5. Let u= w= [-]-[], and w (a) Show that w is not a linear combination of u. (b) Show that u and V…

A: We have to show that-w is not a linear combination of u,u and v are linearly independent,w is a…

Q: Suppose UE 12 V= W= 7 T(u) = 3 8 -5 F=2 T(v) - 3 14

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Q: Suppose T: R³-R² is a linear transformation. Three vectors U₁, U₂ and U3 are given below together…

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Q: Jse a rectangular coordinate system to plot u = T(x) = -|- A. 0 X1 0-1 X₂ Which graph below shows u…

A: Introduction:  linear transformation, in mathematics, a rule for changing one geometric figure (or…

Q: (1)-(9-1²₁.sin(√²²-9)). Find the domain of the vector function, r(t):

A: To find the domain of the given vector function

Q: Find the domain of the vector functions, r(t), listed below. You may use "-INF" for -∞o and use…

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Find scalars x, y and z such that x(2, 1, 4) + y(1,−1, 3) + z(3, 2, 5) = (6,11,6)

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Q: dependent.

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Q: I dont know how to answer this question, it would be very helpful, if you could ans this question…

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Q: Suppose T: R³-R² is a linear transformation. Let u, v and w be the vectors given below, and suppose…

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Q: a. b. Which of the following are linear transformations? 1 2 The function g: M₂,2 (R) → M2,2 (R)…

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Q: Let A(t) = f(t)i + f₂(1) and B(t) = g₁(t)i + g₂(t)},t = [0, 1], where f₁,2, 8₁, 82 are continuous…

A: First we use the condition of parallel vectors and then by intermediate value theorem we will find…

Q: (ii) Let W = span{ } v = and The orthogonal projection of v onto W is projw(v) = and the component…

A: Given : v=-43-7    and W=span{ -2-32 , -3-1-2 } Aim: to find (a) projw(v)      ,and   (b) perpw(v)