Math 1.1 And 1.2

Front 1

Linear Equation

Back 1

An equation that can be written in the form a1x1 + a2x2 + …+ anxn = b,

a,b = number
x = unknowns

Front 2

coefficients

Back 2

real or complex numbers

Front 3

system of linear equations (linear system)

Back 3

a collection of one or more linear equations involving the same variables

Front 4

solution

Back 4

a list (s1, s2,..., sn) of numbers that makes each equation a true statement when the values s1...sn are substituted for x1...xn.

Front 5

solution set

Back 5

The set of all possible solutions

Front 6

Equivalent

Back 6

Linear systems are equivalent if they have the same solution set

Front 7

Consistent

Back 7

A linear system is consistent if it has either one solution or infinitely many solutions

Front 8

Inconsistent

Back 8

A linear system is inconsistent if it has no solution

Front 9

Matrix

Back 9

A rectangular array of numbers

Front 10

Coefficient matrix

Back 10

A matrix who's entries are the coefficients of a linear system

Front 11

Augmented matrix

Back 11

A matrix that contains the coefficients and constants of a linear system

Front 12

Size of matrix

Back 12

Tells how many rows and columns a matrix has

Front 13

m x n matrix

Back 13

m = number of rows
n = number of columns

Front 14

Elementary Row Operations

Back 14

1. Replacement
2. Interchange
3. Scaling

Front 15

Replacement

Back 15

Replace one row by the sum of itself and a multiple of another row

Front 16

Interchange

Back 16

Interchange two rows

Front 17

Scaling

Back 17

Multiple all entries in a row by a nonzero constant

Front 18

Leading Entry

Back 18

leftmost nonzero entry in a nonzero row

Front 19

Echelon form

Back 19

1. All nonzero rows are above any rows of all zeros

2. Each leading entry of a row is in a column to the right of the leading entry of the row above it.

Front 20

Reduced echelon form

Back 20

3. All leading entries are 1

4. Each leading entry is the only nonzero in its column

Front 21

Row Reduced

Back 21

Transformed by elementary row ops

Front 22

Pivot Position

Back 22

Corresponds to a leading entry in the reduced echelon form

Front 23

Pivot

Back 23

is a nonzero number in a pivot position that is used as needed to create zeros via row operations

Front 24

Forward Phase

Back 24

The process that results in an echelon form

Front 25

Backward Phase

Back 25

Last step that turns an echelon form in to a reduced echelon form.

Front 26

Partial Pivoting

Back 26

Selecting the pivot with the largest absolute value, reduces roundoff errors in computers.

Front 27

Basic Variable

Back 27

A variable that corresponds to a pivot column in the coefficient matrix

Front 28

Free variable

Back 28

Any variable in a linear system that isn't a basic variable

Front 29

General Solution

Back 29

A description of all solutions