Linear Algebra Final Exam

consistent
=rightmost col of augmatrix is NOT a pivot col
→
unique
=no free variables
Ax=b has a sol for all b→each b in R is a lin combo of cols of A→cols of A span R→A
has a pivot pos in every row

homogeneous
(Ax=0)has nontrivial sol if/only if the eq has at least 1 free var

linearly independent
=(Ax=0 has only trivial sol→no free variables)(not multiples of
e/o)

linearly dependent
=(at least one vector is a multiple of the other)(#col>#rows)(contains
0vector)

onto(surjective)
=each b in R is the image at least one x (colA span R)

onetoone(injective)
=each b in R is the image of at least one x(only trivial
sol→linearly ind)
if A is
invertible
→Ax=b has unique sol(lin ind)
→ if A is invertible↔injective↔surjective↔bijective
→if detA≠0→A is invertible
→(det(A))(det(B))=det(AB)

Area
=detA

Volume
=detB

area of T(s)
=detA(area of S)

vector space
=nonempty set of vectors defined by addition and scalar multiplication

subspace
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.
 Fall '09
 Linear Algebra, Algebra, Vector Space, lin ind, nontrivial sol, lin ind. eigenvectors

Click to edit the document details