Exercise 6.1.5 Let u ER" be a fixed non-zero vector. The function T defined by T(v) = u + v has the effect of translating all vectors by adding u. Show this is not a linear transformation.

Q: In Question, determine whether T is a linear transformation.

A: Given: T(x)=yxTy. Determine T(x1+x2). T(x1+x2)=yx1+x2Ty=yx1Ty+yx2Ty=T(x1)+T(x2)

Q: 5. T: P3R, T (a₁ + a₁x + a₂x² + a3x³) = a₁ + a₂ Answer

A: Kernel is the elements of P3 whose image under transformation T is zero in R.

Q: (ED) F 3x1 + x2 - 6x3 -x₁ + x₂ +13x3

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Q: Consider the following maps of polynomials S:P →P and T:P→P defined by S(g(x)) = 4 g (5) – g'(-2)and…

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Q: Is this function f a linear transformation?

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Q: T(x, y, z) = (x + y, z-1)

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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: a b L:M,(R)→R’, L 2)-(a+26,b-3c,c+d)

A: First I have written the definition of Linear Transformation , just use this definition for given…

Q: Determine whether the function L: P2 → P2 defined by L(a0 +a1x+a2x2) = a1 +2a2x is a linear…

A: The given function is: L:P2→P2  such that:La0+a1x+a2x2=a1+2a2x

Q: determine if the following transformation is linear or not wwww win i X -y. T:R3--> R? t (y) = %3D…

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Q: r([L1, T2]) = [2x1 – #2, T1 + ¤2, T1 + 3x2]

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Q: Find a formula for the linear transformation whose matrix representation given by

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Q: Explain how to determine whether a function T : V → W is a linear transformation. Secondly give some…

A: We have to explain how to determine whether a function T:V→W is a linear transformation then…

Q: T(xy)=Cax?+by?, cx²+dy²) 2

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Q: Show that u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2) are linearly dependent show all working and explain…

A: Given :u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2)

Q: Find the global transformation matrix to transfer the local coordinate system (x1, y1, z1) to the…

A: Given :-  The global transformation matrix to transfer the local coordinate system x1 , y1 , z1 to…

Q: A ||

A: T:P2→P2 defined by  Tft=f9t+6

Q: Find the bilinear transformation whose fixed points are 1,i and maps 0 to -1.

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Q: Show that projw is a linear transformation and that (projw)² = projw.

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Q: Write a detailed solution to the problem below and upload your answer to Gradescope. Define T: R2 R²…

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Q: [2³] -16 Find k so that there exists a vector X whose image under the linear transformation T(x) =…

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Q: If possible express the vector v as a linear combination of V1, V2, and V3.

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Q: T: P2 P2, .2 T(ax2 + bx + c) = ax² + bx +c B = {1, 1 – x, (1 - x)²} B' = {1, x , x²} v = x² – 3x +3…

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Q: Find the image of the line 2y = x under the transformation with matrix operator

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Q: 3. Let B = Consider T : R2,2 → R²,² defined by T(A) = AB – BA. Let [o o] Bị and B2 :

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Q: I just need an example of a linear transformation V to V that is injective but not surjective

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