Difference between vector and vector space?

[RyozKidz]

can any1 pls tell me or explain the following..?

1.wat is the meaning of trivial solution?
2.wat is the difference between vector and vector space?
3.wat is vector space...?
4.why is the element in a field is called scalar?
5.how to illustrate a vector space over a field?
6.wat is dimension?
7.wat is the meaning of dimensions of the image ??
8.wat is the meaning of rank(A) and null(A)..?
9.watis the use of the rank-nullity theroem ??

 

[Integral]

Do you have any thoughts on these questions to share with us?

 

[maze]

Here are some links you read to learn about these topics.

1.wat is the meaning of trivial solution?
http://www.mathwords.com/t/trivial.htm
https://www.physicsforums.com/showthread.php?t=237796

2.wat is the difference between vector and vector space?
3.wat is vector space...?
5.how to illustrate a vector space over a field?
http://en.wikipedia.org/wiki/Vector_space

4.why is the element in a field is called scalar?
http://en.wikipedia.org/wiki/Scale_factor

6.wat is dimension?
http://en.wikipedia.org/wiki/Hamel_dimension

7.wat is the meaning of dimensions of the image ??
http://en.wikipedia.org/wiki/Column_space

8.wat is the meaning of rank(A) and null(A)..?
http://en.wikipedia.org/wiki/Rank_(linear_algebra )
http://en.wikipedia.org/wiki/Kernel_(matrix )

9.watis the use of the rank-nullity theroem ??
http://en.wikipedia.org/wiki/Rank-nullity_theorem