Chapter 1

Question 0

System

Answer 0

A collection of linear equations involving the same variables

Question 1

Linear equation

Answer 1

Can be written in the form

ax+ay+az…..=b

Question 2

Solution

Answer 2

A list of values that make a system true

Question 3

Solution set

Answer 3

A system of all possible solutions.

Question 4

How many solutions can a system set have

Answer 4

0, 1, of infinite.

Question 5

Coefficient matrix

Answer 5

Records the numbers multiplied by the variables.

Question 6

Augmented matrix

Answer 6

Records all numbers in the system

Question 7

Elementary row operations

Answer 7

Replacement
Interchange
Scaling

Question 8

Row equivalent

Answer 8

If one can be transformed into another by elementary row operations.

Question 9

Leading entry

Answer 9

The first non zero entertaining in a row

Question 10

Echelon form

Answer 10

1 leading entries are in left to right order

2 any all zero row is at the bottom

Question 11

Reduced echelon form

Answer 11

Everything with echelon and
3 all leading entries are 1
4 all leading entries are the only non zeros in there columns

Question 12

Pivot column

Answer 12

A column with a leading entry in echelon form

Question 13

Basic variables

Answer 13

Correspond to a pivot column

Question 14

Free variables

Answer 14

Do not correspond to a pivot column

Question 15

Parametric solution

Answer 15

All basic variables are solved in terms of zero or more free variables.

Question 16

Theorem 2: The existence and uniqueness theorem

Answer 16

1 the system is consistent iff the right-most-column of M is not a pivot column
2 if the system is consistent and all variables are basic variables, then there is only one solution
3 if the system is consistent and has at least one free variable then it has infinite solutions.

Question 17

Column vector

Answer 17

A matrix that consists of only one column

Question 18

Span

Answer 18

Set of all linear combinations.

Question 19

Theorem 4 the following are either all true or all false

Answer 19

1 the equation Ax=b has a solution for every vector b in R^m
2 every vector b in R^m is a linear combination of the columns of A
3 the columns of A span R^m
4 a has a pivot position in every row.