iestion 1. Let V, W be vector spaces and T, S : V → W be linear transformations. Let vị,..., Vm E V. ove that if T(v;) = S(v;) for each i = 1, ..., m, then T(v) = S(v) for all v E span(vı,..., Vm).

Q: (2) For every vector u and vector v in se A) True B False

A: Introduction: Vector is a quantity that has both magnitude and direction. Some mathematical…

Q: Find the vector projection of b onto a when b = (4, 3), a = (2, –1). 7 (2. –1) 1. vector proj. - 7…

A:

Q: Find a vector-valued function whose graph is the plane x+y+z== a. r(u,v)=ui-vj-(3-u-v)k b. r(u,v)=…

A: The equation of plane x+y+z=3

Q: ent, find a linear relation. a) vi = (2, 1, 0), V2 = (0, 1,0), V3 = (-1,2,0) %3D b) wi = (1,2, –2),…

A:

Q: For what value(s) of the parameter p is the vector space described by the set of vectors {v1 = (-1,…

A: Approach to solving the question: Detailed explanation: Examples: Key references:…

Q: 5. Let ū = (-1,3, 2) and i = (1, 1, -1). Find all vectors x' that satisfy u x i = v.

A:

Q: What does is mean for two functions f(x) and g(x) to be orthogonal

A:

Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

A:

Q: 3. Find the to Ihe bae coordinate vector of V relative (l,l, i), ( !!,0), when V= (a,b,c) こ

A: We suppose that (x,y,z) is the coordinate vector of  V relative to given basis so we can write V as…

Q: If T is a mixed tensor, then T} + T{ is generally not a tensor a tensor May or may not

A: Answer : may or may not  Hence, Option (iii) is true.

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: 2. Let S = span{V₁, V2, V3}. Check whether the vector u € St. (a) v₁ = [1, 0, 0, 0], v2 = [0, 3, 0,…

A:

Q: a. b. Which of the following are linear transformations? 1 2 The function g: M₂,2 (R) → M2,2 (R)…

A:

Q: 4) Consider the following three vector spaces with corresponding basis: V₁ =R³ B₁ = {e₁,e2, e3} B₂ =…

A: