Linear algebra question For each vocabulary term listed below, provide both the

Question

Linear algebra question

For each vocabulary term listed below, provide both the formal, rigorous definition, as found in the text, and a brief/informal/casual description that is easier to remember. No symbols. Must be typed. WARNING: copying and pasting another student's work will be considered cheating Excellent work will earn up to 10 bonus points added to your midterm score. 1. span 2. linearly independent 3. one-to-one 4. onto 5. subspace 6. nullspace 7. columnspace 8. rank 9. basis 10. eigenvector 11. eigenvalue 12. lambda-eigenspace

Explanation / Answer

1.Span- The span of a set S of vectors is defined as the intersection W of all subspace Of

V that contain S . So W is the subspace spanned by S or S sons W

A span of S may be understood as the set of all finite linear combinations of the vectors

2. Linear Independent:- A set of vectors is said be linearly independent if no vector in the set can be expressed as linear combination of others

The set of vectors are said be linearly independent if the value of the linear combination is zero but all the coefficients are not simultaneously zero

3.One to One:-A function defined as one to one for which every element of the

range there exist exactly one element in the domain

A function is one to one when the functional values are equal when the points are equal

4.ONTO:-A function from a set to another set is onto if for every element of Coloma in there exist at least one element in the domain

A function is Onto if for every value of range at least one element present in the range

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