Linear Algebra Mat 213

Front 1

Linear equation

Back 1

An equation that can be written as:

a1x1+a2x2+...+anxn=b

Front 2

Coefficents

Back 2

The a's in a linear equation representing real or complex numbers usually known in advance.

Front 3

Linear system

Back 3

Also called a system of linear equations, is a collection of one or more linear equations involving the same variables.

Front 4

Solution

Back 4

Is a list of numbers that makes each equation true when the values are substituted in.

Front 5

Solution set

Back 5

The set containing all the solutions to the linear system.

Front 6

Equivalent

Back 6

2 linear systems are considered equivalent systems if they have the same solution set.

Front 7

Consistent system

Back 7

A system of linear equations with ether one solution or infinitely many solutions.

Front 8

Inconsistent

Back 8

When a system of linear equations has no solution.

Front 9

Matrix

Back 9

A rectangular array of essential numbers.

Front 10

Augmented matrix

Back 10

Contains an extra column containing the restraints from the right side of the equation.

Front 11

Matrix size

Back 11

Is always written as rows then columns.

Front 12

Row equivalent

Back 12

Two matrices are row equivalent if you can transform one into using elementary row operations.

Front 13

Leading entry

Back 13

Refers to the leftmost nonzero entry in any nonzero row.

Front 14

Echelon form

Back 14

Has 3 properties:

1 All nonzero rows are above any all zero rows.

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

3 All entries in a column below a leading entry are zeros.

Front 15

Reduced row Echelon form

Back 15

Has additionally 2 rules:

1 The leading entry in each nonzero row is a one.

2 Each leading one is the only nonzero in its column.

Front 16

Pivot position

Back 16

Corresponds to a leading 1 in the reduced Echelon form.

Front 17

Pivot column

Back 17

A column that contains a pivot position.

Front 18

Pivot

Back 18

The number in the pivot position.

Front 19

Forward phase

Back 19

When you are working the matrix toward the Echelon form.

Front 20

Backward phase

Back 20

When the matrix is in Echelon form and you are working toward reduced row Echelon form.

Front 21

Basic variable

Back 21

The variables in the matrix corasponding to pivot columns.

Front 22

Free variable

Back 22

When a row is reduced to 0x = 0, produces a free variable. Meaning it can be any value.

Front 23

Column vector

Back 23

A matrix comprised of only one column. Also simply called a vector.

Front 24

Equal vectors

Back 24

Are only equal if all entries are in the same order and equal. Order matters for vectors.

Front 25

Vector sum

Back 25

Is obtained by adding the components across or horizontaly.

Front 26

Scalar multiple

Back 26

A constant multiplied to all components of a column vector.

Front 27

Zero vector

Back 27

A column vector whose entries are all 0's.

Front 28

Linear combination

Back 28

Varying multiples of vectors.