Question

please any one tell me what is spanning set in vector space.

Answer 1

sapnning a vector set just means that the linear combination of all the vectors in the set..

Answer 2

can u give me its example please

Answer 3

suppose there are 2 vectors in a set:(x1,y1) and (x2,y2). draw these 2 vectors in your notebook.now take the linear combination of the 2 vector i.e.with the help of these 2 vectors you can draw any vector in the 2d space.

take an example: X=(2,3) and Y=(4,5).now take linear combination of X and Y(any combination).you can make any vector in 2d space.so this set spans 2d space.
similarly set(2,3)and (4,6) spans a line as they are collinear.
you got it??

Answer 4

do u want to say that if v=av1+bv2+.....+kvn and u=au1+bu2+....kun and w=aw1+bw2+....+kwn then we say that u,v,w are the elements of spanning set. am i right?

Answer 5

just a minute..i will attach a file..from that you will understand.just wait

Answer 6

ok

Answer 7

ok..see the file a..in that ther are two vectors a and b..we take linear comb of these two vectors as in file b...like this we can take any lin comb and make any vector in 2d space like in file b i made (3,0). so vector a and b spans 2d space

similarly set(2,3)and (4,6) will form the vectors on a single if we take lin comb of the two vectors..the line pass through 2,3 and 4,6 in every linear combination..so 2,3 and 4,6 spans a line...
is it clear??

Answer 8

ok.can u tell me that each spanning set will form a vector space or not?

Answer 9

also tell me is spanning set is a subspace of vector space or not

Answer 10

i dont have much idea about sub spaces..i am readin about it...will tell u wen i am done..
u have any idea about linear independence??

Answer 11

and is the idea about span clear to u??

Answer 12

yes. thanks a lot