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- StudyBlue
- Wisconsin
- University of Wisconsin - Stevens Point
- Mathematics
- Mathematics 213
- Idk
- chapter 1 vocab

Samantha D.

linear equation

an equation

of the form

a1x1 + a2x2 +. . . + anxn = b

where a1; a2; an and b are real or complex numbers

System of linear equations

collection of one or more linear equations involving the same variables, m eqs n unknowns so

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solution of the system

a list of numbers that makes each eq a true statements when the values are substituted for x

solution set of a system

set of all possible solutions

equivalent

two linear systems that have the same solution set

consistent

if a system has one or many solutions

inconsistent

if a system has no solutions

leading entry

leftmost nonzero entry in a nonzero row

echelon form

- all nonzero rows are above any zero rows
- each leading entry of a row is in a column to the right of the leading entry of the row above it
- all entries in a column below a leading entry are zeros

reduced echelon form

- the leading entry in each nonzero row is 1
- each leading q is the only nonzero entry in its coloumn

pivot position

the position in A that corresponds to the leading q in the reduced echelon form of A

pivot column

a column of A that contains a pivot positon

free variable

a variable that does not correspond to a pivot column in an augmented matrix

Linear combinaton

a sum of scalar multiples of vectors, the scalars are called weights

span

set of all linear combinations

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matrix equation

ax=b

identity matrix

diagnol 1's, 0s everywhere else

homogeneous

if a system can be written in the form Ax=0, has at least the trivial solution

trivial solution

x=0

nontrivial solution

free variables

parametric vector eq

x= su + tv

linearly independent

has only the trivial solution, so no free variables

linearly dependent

has nontrivial solutions so free variables

codomain

the set Rm that contains the range of T. So if v->w, w is the codomain

domain

the set of all vectors x for which T(x) is defined

image

the vector T(x) assigned to x by T in Rm

Range

the set of all images T(x)

onto

if each b in Rm is the image of at least one x in Rn

one to one

if each b in Rm is the image of at most one x in Rn

standard matrix

the matrix A such that T(x)=Ax for all x in the domain of T

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