Recent content by Sasor

0 vector

But what is the importance of containing the origin? Like, what application would having a subspace be good for? Also, what is a basis for it and how is that used in such an interpretation?

Ok, so I understand that a vector space is basically the span of a set of vectors (i.e.) all the possible linear combination vectors of the set of vectors... I don't understand the concept behind a subspace or why it's useful. I know the conditions are: 1. 0 vector must exist in the set...

I don't know how to write out matrices nicely on this forum, but suppose you have some matrices:[1 0 3] [2 0 4] [0 0 5] This would, by definition, be linearly dependent, spanning a plane in r3..is this correct? Since c1=0, c2=anything, c3=0 where c1v1+c2v2+c3v3=0 With this: [1 0 3 5] [3 0...

oh wait, nevermind...domain is in r2...but either way... it wouldn't be onto because you're still only spanning a plane in r3 but if you look at the transformation, matrix, it's linearly independent

well the domain of the matrix is indeed in R3... [3 0] [1 4] [1 0]

Well about that 1-1 but not onto thing, I just did an example- If you want to transform [x1] [x2] -> [3*x1] [x1+4*x2] [x1+5]You'd get a transformation matrix [3 0] ... ...[0] [1 4] *[x1] +[0] [1 0] *[x2] [5] right? in this case, it'd be linearly independent...

Ok cool, and that alternative theorem is very convenient and it makes sense...thanks for the help!

Ok, well linear dependence in context of a matrix is just like linear dependence with a set of vectors... for example [1 4 8 3] [2 4 1 7] [3 2 6 7] If this^ matrix is linearly dependent, then it is equivalent to saying that these vectors: [1] [4] [8] [3] [2] [4] [1] [7] [3],[2],[6],[7] are...

A linearly dependent matrix is a matrix that is linearly dependent matrix...I don't know how I can really explain this...you understand what linear dependence means, right? Also, when I say spans the codomain, I mean that the b in T(x)=b could be any vector in the codomain...

What are you getting at? If I'm incorrect, then just tell me

Hey guys, I'm studying these concepts in linear algebra right now and I was wanting to confirm that my interpretation of it was correct. One to one in algebra means that for every y value, there is only 1 x value for that y value- as in- a function must pass the horizontal line test (Even...

Homework Statement If A is a matrix, find B, a matrix so that AB=BA Homework Equations ? The Attempt at a Solution Solve for inverse?

Ok let me change things to be more readable

Question 1: Homework Statement You have a spring at height d where it is relaxed. You drop a ball (mass m) from a height (h) so that it lands on the spring with spring constant k. What is the max compression of the spring in terms of given variables? Given- m g k d hHomework Equations Find...