B = (v1, v2, V3) is a basis of the vector space V and T :V →V is a linear transformation which satisfies T(vı) = v1 + v2 + 2v3, T(v2) = 2v1 + v2 + 3v3, T(v3) = vị + 2v2 + 3v3. If v = vị – v2 + 2v3 then T(v) = a) vi + 4v2 + 5v3 b) vị – v2 + 2v3 c) 6v1 + 6v2 + 9v3 d) 4v1 + 7v2 +5v3 e) 5v1 + 6v2 + 1lv3

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…

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

A: a)- Given: V=R2 , W=R3 Since R2 is 2-dimensional vector space and  R3 is 3-dimensional vector space,…

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

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

Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V→ R³ be a linear transformation for…

A:

Q: (b) Consider a linear map ƒ: R³ R³3 and suppose the matrix associated with f under the standard…

A:

Q: Suppose T is a linear transformation between vector spaces V and W, with corresponding bases B =…

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Q: (4) V2 = A basis for R³ consists of the three vector V₁ = , V3 = 1 2 3 " (You do not have to verify…

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Q: et B = (b₁,b₂,b3}, D={d₁,d₂} be bases for vector spaces V and W, respectively. et T:V---> W be a…

A:

Q: 3. Determine the standard matrix of a linear transformation in 3D that rotates a vector…

A: Given: Let us consider, Axis =300,Projects on plane x=2y

Q: Let fi = 1+ 2x + 3x², f2 = 2+ 3x + 4x?. B = (f1, f2) is a basis {ao + a1x + a2x²|ao – 2a1 + a2 = 0}…

A: Given f1=1+2x+3x2 and f2=2+3x+4x2. And B=f1,f2 is a basis for the subspace V=a0+a1x+a2x2|a0−2a1+a2=0…

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

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

Q: Let B={b₁,b₂,b3} be a basis for vector space V. Let T: V→ V be a linear transformation with the…

A:

Q: Let B = {b₁,b₂,b3} be a basis for vector space V. Let T:V → V be a linear transformation with the…

A: Linear algebra

Q: (a) Determine whether the vectors vi = (1,1,2), v2 =(1,0,1) and v3 = (2,1,3) span the vector %3D %3D…

A:

Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V→ R³ be a linear transformation for…

A:

Q: 5. Give an example of a linear transformation T from a complex polynomial vector space P to a…

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Q: Let T : R2 → P2 be a linear transformation, and let B= {u1 = [1 2] , u2 = [2 5] }be a basis for R2.…

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Q: 6

A:

Q: (c) Let V and W be given as above. By using linear extension method, determine whether V is…

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Q: Let V₁, V2, and v3 be vectors in a vector space V, and let T:V → R³ be a linear transformation for…

A:

Q: Let V be a vector space and let v, v2, vz e V. Suppose f : V → R³ is a linear transformation and fG)…

A: Given:  f:V→ℝ3 is a linear transformation  fv1=-5-45, fv2=-4-4-2, fv3=-12-4 a. As f is a linear…

Q: Let V be a vector space, and T :V → V a linear transformation such that T(501 + 302) = 4®1 – 402 and…

A: Given  V be a vector space and T:V→V be a linear transformation such that  T5 v1→+3 v2→=4 v1→-4 v2→…

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…

Q: 2. A graph off(x) is shown below. Estimate the area under f(x) in the interval [-3,2] using the…

A: 2 We know that  Ln=b-anf(x0)+f(x1)+...+f(xn-1)Rn=b-anf(x1)+f(x2)+...+f(xn) here, a=-3, b=2, n=5…

Q: Let B = {b₁,b₂, b3} be a basis for a vector space V. Find T(8b₁-5b₂) when T is a linear…

A: We simply use the the defination of matrix representation of linear transformation .

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:

Q: · Let B = {b¡, b2, b3} be a basis for a vector space V. Find T (3b¡ – 4b2) when T is a linear…

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Q: B = (v1, V2, V3) is a basis of the vector space V and T: V → V is a linear transformation which…

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Q: V is a 4-dimensional vector space with basis B = (v1, V2 , V3 , V4). T:V → V is linear…

A:

Q: 4. In the vector space P3(R), let S = {p1(x), p2(x), p3(x)}, where P1 (x) = 63x° + 19x² – 37x – 41,…

A: (a) we see, p2(x) = -3p1(x), so S is not linearly independent. [Ans] (b) As S is not linearly…

Q: Let T : R → R³ be linear transformation. The sequence (v), v2, v3) |) is a basis of R³. If T(v1) =…

A: Given T:R3→R3 be a linear transformation And v1,v2,v3=111,121,112 is a basis of R3. If Tv1=123,…

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.