4. Let B = {õ1, 2, üz} and D = {w1, w2} be bases for the real vector spaces V and W respectively. Let T :V → W be the linear transformation satisfying: T(51) = 201 – w2, T(52) = w1 – w2, and T(53)=w1+202. %3D Determine the dimensions of Ker(T) and R(T). Find bases for these subspaces. Hint: Use a matrix representation.

Q: 2. Let v, = (1,2,1), v2 = (2,9,0), v3 = (3,3,4). Show first that S = {v1, V2, V3} %3D is a basis for…

A: 1. A finite set of vectors v1,v2,...,vn of a vector space V over a field F is said to be linearly…

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A: Here we can use the composition of function formula to find the required values.

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A: Since you have posted multiple question we will solve the first question for you. If you want any…

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A: Introduction: A linear transformation is a characteristic from one vector area to every other that…

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A: Since both T1 and T2 are linear1 Transformation, then for constants c and d, we haveT1(cv + du) = c…

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A: Given two bases b=b1,b2 and f=f1,f2 of ℝ2  where  b1=12, b2=34, f1=11, f2=23 Let Af be a matrix of a…

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A: Given

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

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Q: )* Let T : R³ → R' be a linear transformation for which T(1,1,1) %3D 1,0, 0), T(1,1,0) = (1,3,0, 0),…

A:

Q: Show that the transformation T defined by T(x₁, x₂) = (4x₁2x₂, X₁ +3, 5x₂) is not linear. If T is a…

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Q: Let D = {d1, d2} and B = {b1, b2} be bases for vector spaces V and W, respectively. Let T : V > W be…

A: Bases of two vector spaces and matrix

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Q: Let V be a vector space, v, u E V, and let T₁ : V → V and T₂ : V → V be linear transformations such…

A: The objective of this question is to find the images of vectors v and u under the composite of two…

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Q: #2. Let P be a parallelogram, having area 6 square units, spanned by two linearly independent…

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Q: Let T: P2 → R? be the linear transformation given by T(a + bx + cx?) = (a, a + b+ c). Which of the…

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A: Given :T(v1)=(1,-1,2)T(v2)=(0,3,2)T(v3)=(-3,1,2)

Q: Lett: V→ V' be a linear transformation. Then (1) Ker (t) is a vector sub space of V, and (ii) im (1)…

A: The solution is given as