How are vector spaces viewed as universal algebras?

I have NO IDEA on how to solve this. Exams tomorrow... please help T_T Determine if these are vector spaces. If it is not a vector space, explain what axiom that fail to hold. 1. The set of all 2x2 invertible matrices with the vector addition defined...

I feel the answer is clearly "yes." But my analysis teacher disagrees; I can't fully speak for him, but he says the question has no meaning, as (I believe) he sees C as a one-dimensional vector space over the field C, while he does not see...

Show that union of two sub spaces W1 and W2 of a vector space V is a sub space of V if and only if either W1⊆W2 or W2 ⊆W1? Help me urgently

Precisely, geometric inversion can be regarded on the complex plane without the origin as complex inversion followed by conjugation. At each point, draw the vector corresponding to its image under the transformation -- this defines the vector field.

Let V ve a vector space over a field F A) let x_1.....x_n and y_1......y_n be in V Show that Span(x_1...x_n, y_1....y_x)=Span(x_1..x_n) + Span(y_1....y_n) b) let x_1, x_2, x_3, x_4 be four linearly independent vectors in V. Show that Span(x_1,x_2,x_...

Let V be a vector space. Prove that if it is possible to find m vectors in V which are linearly independent, and n vectors which span V, then m must be less than, or equal to, n. Any help would be appreciated.

Prove the following vector subspaces V and W of R^3 are equal: ...............( 1 ) ( 4 ) V=span ( 2 ) , ( 5 ) .............. ( 3 ) ( 6 ) ..................( 0 ) ( 1 ) ( 5 ) W= span ( 2 ) , ( 0 ) , ( 7 ) .................. ( 4 ) (-1 ) ( 9 ) Really need...