1.1 Systems of Linear Equations

Question 1

linear equation

Answer 1

an equation that can be written in the form a1X1 + … + anXn = b where b and the coefficients a1…an are real/complex numbers

Question 2

linear system / system of linear equations

Answer 2

collection of one or more linear equations involving the same variables

Question 3

solution of a system

Answer 3

a list (s1…sn) of numbers that make each equation a true statement when the values s1…sn are substituted for x1…xn

Question 4

solution set

Answer 4

set of all possible solutions

Question 5

equivalent linear systems

Answer 5

two linear systems are equivalent if they share the same solution set (same as finding the intersection of two lines)

Question 6

consistent

Answer 6

if a system of linear equations has either one or infinitely many solutions

Question 7

inconsistent

Answer 7

if a system of linear equations has no solution

Question 8

matrix

Answer 8

given a system of n equations with m unknowns, a matrix is a rectangular array of n rows (one for each equation) and m columns (one for each unknown)

Question 9

coefficient matrix

Answer 9

matrix consisting of the coefficients of the variables in a set of linear equations

Question 10

augmented matrix

Answer 10

includes the coefficient matrix with a column containing the constants from the right hand side of the equations

Question 11

size

Answer 11

tells how many rows and columns it has (m x n matrix has m rows and n columns)

Question 12

elementary row operations

Answer 12

1. replace one row with the sum of itself and a multiple of another row
2. interchange two rows
3. multiple a row with a nonzero constant