Let T be the map from R? to R' given by T(v) = Av, where A = (a) Find T(v), where v = (b) Find the preimage of (-1,2,9) (c) Show that T is a linear transformation. 3(3,-2).

Q: Let, T:R → R³;T(x, y, z) = (2.x + y, y – z,2y+ 4z) Test whether the transformation T are linear or…

A: This is a linear transformation.

Q: Find the kernel of the linear transformation.T: R3→R3, T(x, y, z) = (−z, −y, −x)

A: Here the given linear transformation Use the definition kernel of the linear transformation

Q: (b) Prove that the mapping T:R2 → R³ from R² into R³, defined by T(x, y) = (x + 1,2y, x + y) is not…

A: A mapping T is a linear transformation if and only if a) T(x+y) = T(x)+T(y) b) T(ax) = aT(x)

Q: Let f:  V-->W be any linear transformation. What are possible solutions to f(0)?

A: Note: A Linear Transformation Maps the Zero vector to the Zero Vector.

Q: Let T be a linear transformation from R2 into R2 such that T(1, 0) = (1, 1) and T(0, 1) = (-1, 1).…

A: Let us consider a linear transformation T: V→W and T(v1)=w1, T(v2)=w2 Then any element u in v can be…

Q: Determine whether Lis linear transformation L:R → R° is reflection with respect to y-axis.

A: L:R2→R2 is reflection with respect to y-axis

Q: Find the image of the point (-2,4) under the affine transformation T(x) = x + (5, – 1).

A:

Q: 1. Let L: M2R be defined by (:2)---d+b-c. a Is La linear transformation? Explain.

A:

Q: give a counterexample to show that the given transformation is not a linear transformation.

A: Let,

Q: Sketch the image of the triangle with vertices (0,0 , 1,0 and 0,1 ) ( ) ( ) under the given…

A: Given: Vertices (0, 0), (1, 0), and (0, 1) T(x, y) = (2x, y)

Q: T is a linear transformation from R² into R². Show that T is invertible and find a formula for

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Q: Let P : R³ → R³ be the linear transformation defined as the projection onto span{ū, ū2}, where 1…

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Q: What are the coordinates of U' for the transformation (T-3, 1) ° D4) (ATUV) of T(-7, –6), Ú(-8, 3),…

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Q: Give a counterexample to show that the given transformation is not a linear transformation.

A: To show this T xy=|x||y| is not linear transformation by counter example.

Q: . Find the image of the line that passes through the point (1, 1) and is parallel to the under the…

A: Here is the solution of the given problem.

Q: Use the definition of the sum of two linear transformations directly to compute (T1 + T2)((x, y,…

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

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Q: What kind of transformation results in applying the rule (x, y) → (x + 5, y)?

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Q: If T : V → W and U : W → Z are linear transformations, prove that rank(UT) < rank(T). (Hint: How…

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Q: Give a counterexample to show that the given transformation is not a linear transformation.

A: Given         T xy = xyx+y

Q: give a counterexample to show that the given transformation is not a linear transformation.

A: Given,   A linear transformation,

Q: Let T: R2 R² be such that cos 0 - sin 0 cos e sin 0 How that T is an orthogonal linear…

A:

Q: а) Т. М22- M22 defined by T .C 4 Identify that it is Linear or Non-Linear Transformation.

A: Given: T:M22→M22is defined by: Tabcd=1-124abcd So,  Tabcd=a-cb-d2a+4c2b+4d Now,  Let α=a1b1c1d1 ,…

Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: Find the kernel of the linear transformation.T: R3→R3, T(x, y, z) = (x, 0, z)

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Q: Let Co,4, be the vector space of continuous functions mapping the interval 0 <x< 4 into R. Let T :…

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Q: 8. Show that the mapping T: V,(R) → V½(R) defined = (3a, - 2az + az3, a1 – 3a, – 2az3) is a linear…

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Q: Let F: R3 → R4 be a linear transformation.   f (x, y, z) = (x, x + 3y, x, x + z) Is f bijective?

A: A function f is said to be bijective if and only if it is both injective(one to one) and surjective…

Q: such that M2,2 into Let T be a linear transformation from M, 2 (::)-(: :) (::)-(:: (::)-[::} (::)-[:…

A:

Q: Find the image of the Z-shaped figure at right with vertices (0, 0), (6, 0), (6, 6), and (0, 6)…

A: Now , we have got 4 points .  We first try to find the image of those points then plot them on the…

Q: Let u = u(x, y) By using the transformation r = -2x + y2 find uxy = s = 2x + y?,

A: Let u=u(x,y) And transformations  r=-2x+y2 s = 2x+y2 To determine uxy uxy=urrrxry +…

Q: 9. Show that the function T: R³ → R3 defined by T(r, y, z) = (x – z, 2x + y, 2y – 3x) %3D is a…

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

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Q: Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the…

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Q: Find the area.

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Q: give a counterexample to show that the given transformation is not a linear transformation.

A: Given,  The transformation

Q: Calculate the nullity 7(T) for the linear transformation T defined by T(x, y, z) = (x +2y + z, -1 +…

A: Determine the span of the function. Now use it to determine the dimension of N(T). Now use the…

Q: Give a counterexample to show that the given transformation is not a linear transformation.

A: Given transformation is Txy=x+yx-y To prove a linear transformation the properties are…

Q: 1. Let L: M2 - R be defined by ((: :)- = a -d+b-c. Is La linear transformation? Explain.

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Q: ask question

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Q: Suppose T:R2 → R² is defined by T(x,y) = (x - y, x+2y) then T is .a Linear transformation .b…

A: The solution is given as

Q: Find the kernel of the linear transformation.T: R3→R3, T(x, y, z) = (0, 0, 0)

A: Let T:V→W be a linear transformation. Then the set of all vectors v in V that satisfy Tv=0 is the…

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: Let T1, T2 : V → V be linear transformations satisfying Tị • T2 = ly (where 1y denotes the identity…

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Q: 1. Find the image of the line that passes through the point (1, 1) and is parallel to the = under…

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Q: of the transfo ) Check whether the linear transformation given by T(z, y, :) (- 4y +2, 2r +y+ 3:, 5r…

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

Q: Q4:A. Find vector field of {(1,0), (1, 1), (1,-1), (-1,0),(-1,-1)] For transformation f(x,y) = (1,2)

A: Given that: 1,0,1,1,1,-1,-1,0,-1,-1 for transformation f⇀x,y=1,2. The objective is to determine the…

Q: Find the linear fractional transformation that maps (1, 0, i) to (1, 0, 1+i).

A: The formula for transformation is given by: w-w1w-w3·w2-w3w2-w1=z-z1z2-z3z-z3z2-z1 Here, w1=1, w2=0,…

Q: Sketch the image of the rectangle with vertices at (0, 0), (1, 0), (1, 2), and (0, 2) under the…

A: Definition used -                 Image of a rectangle with given vertices can be found by a given…