{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

solutionsFinalExam

# solutionsFinalExam - Math 222 500 1 Final Exam(25 Define...

This preview shows pages 1–2. Sign up to view the full content.

Final Exam Dec 13, 2006 1 . (25) Define the following: a . L is a linear transformation, L is first of all a function mapping a vector space V into a vector space W with the following additional property: if x u and y u are any two vectors in V and u and U are any two scalars, then L u u x u U U y u U ± u L u x u U U U L u y u U . b . matrix representation of a linear transformation, Let L : V ² W be a linear transformation. Suppose B 1 and B 2 are bases of V and W respectively. Then A is the matrix representation of L with respect to the given bases if ± L u x u B 2 ± A ± x u ² B 1 . c . linearly independent set of vectors, A set of vectors ³ x u i ´ i ± 1 n is linearly independent if whenever c 1 x u 1 U µ c n x u n ± 0 u , then each of the c i ’s must equal 0. d . eigenvector If A is an n ± n matrix and x u u R n , then x u is an eigenvector of A if x u U 0 u and there is a number ² such that Ax u ± ² x u . e

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

solutionsFinalExam - Math 222 500 1 Final Exam(25 Define...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online