Question

Let F be the field of two elements and let V be a two dimensional vector...

Let F be the field of two elements and let V be a two dimensional vector space over F. How many vectors are there in V?How many one dimensional subspaces? How many different bases are there?

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let T:V→V be an endomorphism of a finite dimensional vector space over the field Z/pZ with...
Let T:V→V be an endomorphism of a finite dimensional vector space over the field Z/pZ with p elements, satisfying the equation Tp=T. Show that T is diagonalisable.
Let V be an n-dimensional vector space. Let W and W2 be unequal subspaces of V,...
Let V be an n-dimensional vector space. Let W and W2 be unequal subspaces of V, each of dimension n - 1. Prove that V =W1 + W2 and dim(Win W2) = n - 2.
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...
Let V and W be finite-dimensional vector spaces over F, and let φ : V →...
Let V and W be finite-dimensional vector spaces over F, and let φ : V → W be a linear transformation. Let dim(ker(φ)) = k, dim(V ) = n, and 0 < k < n. A basis of ker(φ), {v1, . . . , vk}, can be extended to a basis of V , {v1, . . . , vk, vk+1, . . . , vn}, for some vectors vk+1, . . . , vn ∈ V . Prove that...
Let U and W be subspaces of a nite dimensional vector space V such that U...
Let U and W be subspaces of a nite dimensional vector space V such that U ∩ W = {~0}. Dene their sum U + W := {u + w | u ∈ U, w ∈ W}. (1) Prove that U + W is a subspace of V . (2) Let U = {u1, . . . , ur} and W = {w1, . . . , ws} be bases of U and W respectively. Prove that U ∪ W...
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.
Let V be a vector space and let U1, U2 be two subspaces of V ....
Let V be a vector space and let U1, U2 be two subspaces of V . Show that U1 ∩ U2 is a subspace of V . By giving an example, show that U1 ∪ U2 is in general not a subspace of V .
(3) Let V be a finite dimensional vector space, and let T: V® V be a...
(3) Let V be a finite dimensional vector space, and let T: V® V be a linear transformation such that rk(T) = rk(T2). a) Show that ker(T) = ker(T2). b) Show that 0 is the only vector that lies in both the null space of T, and the range space of T
Let V be a finite-dimensional vector space and let T be a linear map in L(V,...
Let V be a finite-dimensional vector space and let T be a linear map in L(V, V ). Suppose that dim(range(T 2 )) = dim(range(T)). Prove that the range and null space of T have only the zero vector in common
Let V be a vector space: d) Suppose that V is finite-dimensional, and let S be...
Let V be a vector space: d) Suppose that V is finite-dimensional, and let S be a set of inner products on V that is (when viewed as a subset of B(V)) linearly independent. Prove that S must be finite e) Exhibit an infinite linearly independent set of inner products on R(x), the vector space of all polynomials with real coefficients.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT