Question

what is a span , basis and and subspace ? , if C spans B and B spans A . SUCH THAT A , B ,C ARE VECTORS IN A SUBSPACE D ? .

Answer 1

I will First Clear Your Doubt on BASIS AND SUBSPACE

Answer 2

1. Do the vectors
j1
= (1,0,-1,2) and
j2
= (0,1,1,2) form a basis for the space W = {(a,b,c,d) l a - b + c = 0, -2a - 2b + d =0} ?

Answer 3

answer:1. i substitute each vector in a,b,c,d equation and find the equality, so happen when i substitute in all returns 0, which implies that it does form a basis. Is there a proper working for this, cause i can do this by inspection.

Answer 4

2 BASIS
Find a basis for \[W = { (a,b,c,d) : a - b + 2d = 0 , 3a + c + 3d = 0 }\]

Answer 5

answer: I was wondering forming a matrix and row reduced the matrix and get a linear dependence equation and plug in some value for c & d to find a & b.

Answer 6

3. Find the dimension of the following subspaces of
R^3

Answer 7

hint: First, recall the definition of dimension. The dimension of a subspace is the number of linearly independent vectors which span the given subspaces, ie. the number of vectors in the basis of these subspaces. The vectors in any given basis are all linearly independent. Do you see what to do now?

Answer 8

4. Suppose that a subspace W
⊂
R^3
has a basis { (1,2,3),(1,0,1) }.
a)Is { (-1,-2,-3), (3,2,5) } a basis for W? Why?

Answer 9

answer: HINT:
Suppose you are given a basis and another basis which may or may not span the same subspace as that of the first. Informally, if you can express every vector in the first group of vectors as a linear combination of the vectors in the second group, what does that tell you about the corresponding subspace spanned by the latter group with respect to the first?

Answer 10

if d spans c , where c spans a and , b , i think we can represent every vector in a , b,and c as a linear combination of vectors in d . can we ?

Answer 11

yes! but my brother you should visit this: http://www.khanacademy.org/math/linear-algebra/v/linear-combinations-and-span

Answer 12

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Answer 13

say we choose d in R3 to be (1,2,3,) such that we find any vectors in a ,b,c to represent d

Answer 14

ya!

Answer 15

thanks jo , do you know phsyics i am strugling with a question here ?

Answer 16

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Answer 17

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Answer 18

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Answer 19

help