Question

Linear Algebra: Using the 10 Vector Space Axioms, prove that if u is a vector in...

Linear Algebra:

Using the 10 Vector Space Axioms, prove that if u is a vector in vector space V, then 0u=0

State which Axiom applies to each step of the proof

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let T be a 1-1 linear transformation from a vector space V to a vector space...
Let T be a 1-1 linear transformation from a vector space V to a vector space W. If the vectors u, v and w are linearly independent in V, prove that T(u), T(v), T(w) are linearly independent in W
Suppose that, in some vector space V , a vector u ∈V has the property that...
Suppose that, in some vector space V , a vector u ∈V has the property that u+v = v for some v ∈ V . Prove that u = 0.
4. Prove the Following: a. Prove that if V is a vector space with subspace W...
4. Prove the Following: a. Prove that if V is a vector space with subspace W ⊂ V, and if U ⊂ W is a subspace of the vector space W, then U is also a subspace of V b. Given span of a finite collection of vectors {v1, . . . , vn} ⊂ V as follows: Span(v1, . . . , vn) := {a1v1 + · · · + anvn : ai are scalars in the scalar field}...
Let u, vand w be linearly dependent vectors in a vector space V. Prove that for...
Let u, vand w be linearly dependent vectors in a vector space V. Prove that for any vector z in V whatsoever, the vectors u, v, w and z are linearly dependent.
Let V be an n-dimensional vector space and W a vector space that is isomorphic to...
Let V be an n-dimensional vector space and W a vector space that is isomorphic to V. Prove that W is also n-dimensional. Give a clear, detailed, step-by-step argument using the definitions of "dimension" and "isomorphic" the Definiton of isomorphic:  Let V be an n-dimensional vector space and W a vector space that is isomorphic to V. Prove that W is also n-dimensional. Give a clear, detailed, step-by-step argument using the definitions of "dimension" and "isomorphic" The Definition of dimenion: the...
Using a step by step proof format Please prove: Given that x is a vector in...
Using a step by step proof format Please prove: Given that x is a vector in the span of V, where V is a linearly independent set of vectors, show that there is ONLY ONE linear combination of the vectors in V that yields x. (Hint: to show that something is unique, assume that there is more than one such thing and show that this leads to a contradiction)
Suppose that V is a vector space with basis {u, v, w}. Suppose that T is...
Suppose that V is a vector space with basis {u, v, w}. Suppose that T is a linear transformation from V to W and suppose also that {T(u), T(v), T(w)} is a basis for W. Prove from the definitions that T is both 1-1 and onto.
Suppose V is a vector space and T is a linear operator. Prove by induction that...
Suppose V is a vector space and T is a linear operator. Prove by induction that for all natural numbers n, if c is an eigenvalue of T then c^n is an eigenvalue of T^n.
a)Suppose U is a nonempty subset of the vector space V over field F. Prove that...
a)Suppose U is a nonempty subset of the vector space V over field F. Prove that U is a subspace if and only if cv + w ∈ U for any c ∈ F and any v, w ∈ U b)Give an example to show that the union of two subspaces of V is not necessarily a subspace.
Hi. I have two questions about the linear algebra. 1. Prove that a linear transform always...
Hi. I have two questions about the linear algebra. 1. Prove that a linear transform always maps 0 to 0. 2. Suppose that S = {x, y, z} is a linearly dependent set. Prove that every vector v in the span of the set S can be expressed as a linear combination in more than one way. Will thumb up for both answers. Thank you so much!