Let T:R3 → R³ be a linear transformation such that T(1,0,0)=(4,–1,2) T(0,1,0)=(1,–2,3) , and T(0,0,1)=(2,–2,0) .what is T(1,–4,2) ? О (6, 1, -4) (6, -1, -4) О(4, 3, -10) (4, -13, 10)

Q: 1. If T(x,x,,x,) =(4x, – 2x, +5x,,x, - 7x,,6x, – 3x, – x,) is a linear transformation from ~3, find…

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Q: Let T : R" → R" be a linear transformation such that T(5v1 – 352) = –5v1 + 302 and T(–371 + 202) =…

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Q: Suppose T is a linear transformation, where T(ü) T(5) T(w) (1, 0, 0) (- 3, – 5) %3D %3D (– 5, – 3)…

A: u→=<1,0,0>       T(u→)=<-3,-5>v→=<0,1,0>       T(v→)=<-5,-3>w→=<0,0,1>…

Q: Let T: R-R be a linear transformation such that T(1, 0, 0) - (4, -1, 2), T(o, 1, 0) = (1, 3, -2),…

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Q: Let T : P2 → P, be the linear transformation defined by T(ax? + bx + c) d -(ax² + bx + c). dx T(3x?…

A: Topic - linear transformation

Q: Let 7: R→ R be a linear transformation such that 7(1, 1, 1) = (4, 0, -1), 7(0, -1, 2) = (-5, 5, -1),…

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Q: Let L : R → R² be a linear transformation such that L(1,0,0)") = (2, 2)", L((0, 2, 0)") (-3, –5)",…

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Q: 4. Consider two 3 × 3 matrices A and B with det(A) = -2 and det(B) = -1. Let T(*) = Až be a linear…

A: solution :-

Q: 8. Let T: R³ → R² be a linear transformation and suppose T(0, 0, 1) = (2, 1), T(0, 1, 1) = (0,5),…

A: Let  be a linear transformation and suppose  and . The objective is to determine..

Q: Let T : R² R2 be a linear transformation such that T(x₁, x₂) Find x = (1, 2) such that T(x)…

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Q: into M2, such that M2,2 Let T be a linear transformation from (::)-[: (::)-[ 0 1 0 2 1 2 0 1 1 0 1 3…

A: Solution

Q: 11. Explain whether there exists a linear transformation T:R. → R2 such that T(0, 1, 1, 1) = (2,0),…

A: A transformation is called linearly independent when the nullity of the transformation is 0.…

Q: Let T: R3 → R3 be a linear transformation such that T(1, o, 0) = (4, –1, 2), T(0, 1, 0) = (1, 3,…

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Q: 2. Let T: R³ R² be a linear transformation such that Find T(1,2,1)= (1,0) T(2,9,0)= (-1,1) T(3,3,4)=…

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Q: Let T: R3 → R3 be a linear transformation such that T(1, 0, 0) = (4, -1, 2), T(0, 1, 0) = (-2, 1,…

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Q: Let T: R -R be a linear transformation such that T(1, 1, 1) = (5, 0, -1), T(0, -1, 2) = (-5, 4, -1),…

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Q: 21. Let T R² T(x1, x₂) T(x) = R2 be a linear transformation such that (x₁ + x2, 4x₁ + 5x2). Find x…

A: Please check the answer in the next step. This is very straight forward.

Q: 5. Let T: R³ R2 be the transformation defined by T (:) - = (3x - 2y + 4z 5x - 9z +42) Is T is a…

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Q: Suppose T is a linear transformation, where (4, – 3) (– 1, – 5) (- 1,5) (1, 0, 0) T(ü) T(7) T(w) %3D…

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Q: Suppose T is a linear transformation, where (1, 0, 0) T(ü) (- 3, 2) (0, 1, 0) T(7) (5, 4) (0,0, 1)…

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Q: Let T: R³ – R³ be a linear transformation such that T(1, 0, 0) = (-1, 2, 4), T(0, 1, 0) = (-2, 1,…

A: Linear Transformation :   Let U(F) and V(F) be two vector space. Then a mapping T:U→V is called…

Q: 1. (a) Define: invertible linear transformation. (b) T: (7₁,72) → (67₁ - 872,-57₁ +77₂) is a linear…

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Q: Let f : R² → R² be the linear transformation defined by f(x) = х. B = {{-1,2) , (–2, 3)}, c =…

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Q: Suppose T is a linear transformation, where (1,0, 0) T(u) (4, – 5) %3D %3D (0, 1, 0) (- 3, – 5) (-…

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