Math Is Fun Forum

For the question:
Give a basis for the vector space V and find the dimension of V

I could only find x in which this would work.

So would the basis be {x}??

I would appreciate some guidance rather than a direct answer(if this is possible=)) since this is an assignment question.

Thanks all

This is Theorem 5.2

Let V be a vector space and let W be a nonempty subset of V. Then w is a subspace of V if and only if the following conditions hold:

a. If u and v are in W, then u + v is in W.
b. If u is in W and c is a scalar, then cu is in W.

Now for the question:

In exercise 25, use Theorem 5.2 to determine whether W is a subspace of V.

Can someone please explain to me what is going on here, thanks   (if it makes a difference the column vector above is also ment to have squigly brackets around it, but i couldnt do that AND the parenthesis.)

Hi can anyone explain a method to solve this problem

let A,B be two matrices where

A=[1,0,-2;-3,1,1;2,0,-1]  (where ; seperates the rows of the matrix)
B=[2,3,0;1,-1,1;-1,6,4]

Use the matrix-column representation of the product to write each column of BA as a linear combination of the columns of B.

cheers guys

I'm having a few troubles with 'validly deduce'

Here is the question:

Q: For any set S of sentences, if T is a tautology, then you can validly deduce T from S.

Can anyone explain to me what it is to 'validly deduce' something, pretty confused here, cheers