Let D be the vector space of all differentiable functions mapping R into R. Let V be the subspace of D defined by V = sp(x? e* , xe* , e* ). Define the linear transformation T: V –V by T(f) =f*the derivative of f. Let ordered bases for V be B = B' = (x² e*, xe", e* ). Find the matrix representation A of T relative to B, B’. Then use A to compute T(f), where f(x) = 3x² ex – 4xe* + 2e*.

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A: Consider the given information: H=2,0,1,2,-3,0 be the subspace in R3. T:R3→R4 defined by,…

Q: Find the dimension of the vector space U of all linear transformations of V into W for each of the…

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A: In linear algebra, the kernel of a linear transformation is also known as the "null space." Given a…

Q: b) Let U = {(x,y,z) : 2x+3y +z = 0} and V= {(x,y,z): x + 2y-z = 0} be the subspaces of R3. Find a…

A: This is a problem of linear transformation.

Q: Let T: V-->W be a linear transforma­tion between finite-dimensional vector spaces V and W Let B…

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Q: What is the matrix P = (P₁) for the projection of R³ onto the subspace V spanned by the vectors a₁ =…

A:

Q: Let T: V-->W be a linear transforma­tion between finite-dimensional vector spaces V and W Let B…

A: Let V and W be vector spaces and B and C are bases for V and W respectively and let T be linear…

Q: 27. Let W = sp(ex, ex, esx) be the subspace of the vector space of all real-valued functions with…

A:

Q: ar Transformations y (7) + rank (T) = dim (V) in this case, namely,

A:

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A:

Q: 5. Let W be the subspace of the vector space V = R spanned by the vectors =(1,3, 1, -2), B = (-3,…

A:

Q: Let B = {1, x, eX, xe*} be a basis for a subspace W of the space of continuous functions, and let Dx…

A:

Q: Let V be the vector space of all polynomials in the variable x over R. Show that the mappings…

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Q: . Consider M₂ (R) as a vector space and its subspaces U₁= {A € M₂(R): A¹ = A} and U₂ = {A € M₂(R) :…

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A:

Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

A: Solution

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A: We have to find the transition matrix S using the differentiation operator on the vector space V and…

Q: Let & denote the vector space of all functions &: R&R under the usual operations of function…

A: B=sint, cost is a basis of H

Q: Let T be a linear transformation from V to W. Prove that the imageof V under T is a subspace of W.

A:

Q: Let V be a finit dimensions vector space of at least dim =1, Let T: V-> V be a linear transformation…

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A:

Q: Consider the vector space of all real-valued differentiable functions, and let V denote its subspace…

A:

Q: Describe all linear maps ƒ : R² → R² that are projections with image the subspace ((1,2)).

A: f: ℝ2→ℝ2Subspace =1, 2

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A: here we can use simple conditions that if a linear function preserve scalar multiplication and…

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A: We have to prove given result:

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A:

Q: Be F1(x, x, x) e R³ and F2(a, b,0) e R³ a)show that F1 and F2 are subspaces of R3 b)show that R' =…

A: Solution of the problem as follows

Q: Let T: R^3 --> R^3 be the linear transformation represented by the matrix in the image. (a) Let…

A: M=-4372-1-321-1

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.