Q2. Let T: R³ R³ be a transformation defined by - ()-() T (a) Is T a linear transformation? Justify your answer! (b) If T is a linear transformation, find the matrix of T. POP 2

Q: T: M2x2(R) → R³ is a linear transformation which satisfies 7(: ) ‚T 7(; :) - 7(: )- T „T Determine T…

A: The given transformation is given as: T:M2×2ℝ→ℝ5T1111=10001,T1222=11002T1323=12113,T1324=12324

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: Let T be a linear transformation from R2 into R² such that 7(1, 0) = (1, 1) and 7(0, 1) = (-1, 1).…

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

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Q: Show that the transformation T defined by T[x1, X2) = (2x, - 3x.2, Xq + 4, 5x,) is not linear. %3D

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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: Let T1 : P2 → R² and T2 : R? → R2x2 be linear transformations defined as follows. a + b b - T1(ax? +…

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Q: Which of the following transformations are linear? yi X1 + 10 A. X2 8x1 Y2 %D yı %D Y2 7 yı 3x1 + x2…

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Q: ). Find T(1, 3) and 7(1, -5).

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Q: Consider the following function. T: M22 → M₂2 defined by T [W]-[²] y -y Find the following images of…

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Q: Determine if the following transformations are linear. a)T(x, y) = (4x-6y,-2x +3y) b)T(x, y, z) =…

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Q: find a linear transformation that T:R2 -> R3 T(1, 2) = (1, -1, 2) T(1, 3) = (3, 0, 1) T(1, 1) =…

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Q: 6. Show that T is a linear transformation. T(x1, x2) = (2x2 – 3x1, x₁ - 4x2, 0, x₂).

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Q: then T If T: R³ R³ is a linear transformation such that -5 *(Q)-⠀··(8)-¦··(8-E] T T T 2 0

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Q: 6. Let T be a linear transformation from R to R?given by T(x, x2x3) = (3x1 - 5x2 + X3, X1 + 6X3)…

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Q: Solve the 2 31 -30-8 Let A= 8 -7 5 and u- 2 Define a transformation T: R³ -> by T(x) = Ax. Find…

A: As per guidelines we are allowed to solve maxim one questions at a time.kindly post another…

Q: B) IR2 --> IR3           (x, y) --> (x, y2, x+y) Is it linear transformation? investigate.

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Q: Suppose that T is a linear transformation, with T(u,) = T(u2) =:: Find T(2u, - 3u,).

A: From the definition of linear transformation we can solve this question.

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

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Q: (1 point) Find the matrix M of the linear transformation T :R² → R² given by 7(E)- 5x1 + (-6) x2 T…

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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: T(1,0) =(1,1) T(0,1) = (-1,1)

Q: Let T1 : P2 → R² and T2 : R → R2x2 be linear transformations defined as follows. a +b] Ti (аx? + bx…

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

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Q: (x- 2a 2b (ах + by + c), у — 2. Verify that the mapping (x, y)→ is a transformation. -(ах + by + c)…

A: Given: The mapping; x,y↦x-2aa2+b2ax+by+c,y-2ba2+b2ax+by+c   To verify: The given mapping is a…

Q: Q3-B: Verify the Kummer transformation: U(a,c;x) = x¹-U(a-c+1,2-c;x)

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