Let a bilinear transformation be a bilinear form ß: R² x R² R by B(x, y) = X1₁ V₁, and x = (x1, x2) and y = (y1, y2). (suppose we already proved that B is indeed bilinear.) Find an example of a linear transformation T: R² → R² such that B(L(x), L(y)) = B(x, y) for all x, y belong to R², but L is not bijective.

Q: Find x such that T(x) = (7,12).

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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: Find the Jacobian J of the transformation T(u, v, w) = (-3u +5v-3w, 2u+4v+3w, 4u+v=4w) = (x, y, z).…

A: Given:- Tu,v,w=-3u+5v-3w,2u+4v+3w,4u+v-4w=x,y,z

Q: Let f : R² → R be defined by f((x, y)) = 7x - 2y. Is f a linear transformation? a. f((x₁, y₁) + (x2,…

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Q: If T is a linear transformation and T(u), T(v), T(w) are linearly independent, then u, v, w are…

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Q: Let T: P2 P, be the linear transformation given by T(1) = x, T(x) =-x,T(x+x) = x2. Then a basis for…

A: The given linear transformation: Given transformations: To find the basis of kerT: The formula for…

Q: 9. True or False. Justify your answer. (A) Let T : V → W be a linear transformation and {v1, · · ,…

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Q: Let T: R → R" be a linear transformation such that T(2v₁ – 3v₂) = 2v₁ – 3v2 and T(−3v₁ + 5v₂) = 4v₁…

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Q: V₁ = (1,0), and let T: R² → R4 be the linear transformation T(v₁) = (6,0,3,1), Compute T(-3,2). V₂ =…

A: we need to compute T(-3, 2).

Q: Let T: R³ → R² be a linear transformation. If u and v are vectors in R² such that T(u) [3], and T(v)…

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Q: Let T: R³ R³ be a linear transformation defined by T(x, y, z) = (x+y.y-2z, x-3y + 4z), (BUATED. nd B…

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Q: Let T :U → V be a linear transformation. Use the rank-nullity theorem to complete the information in…

A: The given table is - We know that dim(U) = dim ℝm×n = m×n For ℝ1×2 dim (U) = 2 Using rank nullity…

Q: d) Let T: R² R² be a linear transformation given by T(x, y) = (x + y, x - y). Given the bases B =…

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Q: Let f: R² → R be defined by f((x, y)) = 6x- -9y - 9. Is f a linear transformation? a. f((x1, y₁) +…

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Q: Prove that T: ℝ2 → ℝ2 is a linear transformation and find the inverse, if it exists. T(x,y) = (2x+y,…

A: Given a linear transformation T:R2→R2 defined by T(x,y)=(2x+y,-x+y).

Q: Let T: R³ R³ be the linear transformation defined by T(x₁, x2, X3) = (x1 — X2, X2 - - 3 Find a…

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Q: Let T: R² →R² be a linear transformation such that T (×₁,×₂) = (x₁ + x₂, 2x₁ +4x2). Find x such that…

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Q: The linear transformation T: R³ → R² is defined by T(x)= Ax, where 0-27 A 10 0 11 Find ker(7).…

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Q: Let T: R2→R? be a linear transformation such that T (x,X2) = (X1 +x2, 4x, +3x2) . Find x such that…

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Q: Letf: R² → R be defined by f((x, y)) = 6x − 7y. Is f a linear transformation? a. f((x₁, y₁) + (x2,…

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Q: Show that the map t: V₂(R) → V3(R) defined by t(a, b) = (a + b, a - b, b) is a linear…

A: We have given a map , t : V2R → V3R  defined by ,  ta ,  b = a + b , a - b , b We need to show that…