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

A:

Q: Consider the vector v = 1 + 4t in terms of the standard basis for P2, {1, t, t²} and new basis B =…

A:

Q: V is a 3-dimensional vector space with basis By (V1, V2, V3) and W is a 3-dimensional vector space…

A:

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

A:

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: 5.- Demonstrate whether the vectors of the following vector space are linearly dependent or linearly…

A:

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 = (1, x, x², x*) be an ordered basis for P3. Find the coordinate vector of 8x – 6x2 – 9x + 3…

A:

Q: B = (v1, v2, v3) is a basis of the vector space V and T: V → V is a linear transformation which…

A:

Q: 1. Let D= {d1,d2, d3} and F= {f1, f2, f3} be bases for vector space V, and suppose f1 = 2d1 – d2 +…

A: 1) Given that D=d1,d2,d3F=f1,f2,f3f1=2d1-d2+d3f2=3d2+d3f3=-d1+2d3 To find (a) and (b):

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

A:

Q: 6

A:

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

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

A:

Q: The cross product of two vectors in R³ is defined by Let = A = 5 a1 a2 az xb₂ = b3 a₂b3 - a3b2 a3b1…

A:

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: Show that the vectors p1(x) = a + bx and p2(x) = c + dx are linearly independent in P1(R) if and…

A:

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

A:

Q: Let V be a vector space, and T :V →V a linear transformation such that T(5v1 + 302) = 40, – 402 and…

A: If you have any doubts in the solution please ask me  in comments i will reply you as soon as…

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.