1.1 Introduction to Systems of Linear Equations

Question 1

linear equation

Answer 1

an equation with variables and constants with a degree of 1

Question 2

homogeneous linear equation

Answer 2

a set of linear equations where the right-hand side of each equation is 0

Question 3

linear system

Answer 3

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

Question 4

unknowns

Answer 4

a variable, which is a placeholder for an unknown quantity in an equation

Question 5

solution

Answer 5

a set of values for the variables in a system of linear equations that satisfies each equation

Question 6

ordered n-tuple

Answer 6

an ordered sequence of natural numbers where n is greater than 1

Question 7

consistent

Answer 7

a system of equations is consistent if there is at least one set of values that satisfies all equations in the system

Question 8

inconsistent

Answer 8

a system of equations that has no solution

Question 9

parameter

Answer 9

a variable for which the range of possible values identifies a collection of distinct cases in a problem

Question 10

parametric equations

Answer 10

define x and y as functions of a third parameter, t (time)

Question 11

augmented matrix

Answer 11

each row represents one equation in the system and each column represents a variable or the constant terms

Question 12

elementary row operations

Answer 12

operations that are performed on rows of a matrix