1.1 Systems of Linear Equations Flashcards
what is a linear equation?
an equation written in the form a1x1+a2x2+anxn..=b
b and coefficients a are complex numbers
n is a positive integer
what is a system of linear equations?
A collection of linear equations that has around the same variables
What is a solution?
When a system has a list of numbers, s1, s2, sn that makes each equation in the system a true statement when substituted for x1, x2, xn
What is the Solution set?
All possible solutions of a system
What does equivalent mean in terms of Linear systems?
When two linear systems have the same Solution set
What does it mean graphically when two sets of linear systems are equivalent?
Where are those two lines intersect
What are the three types of solutions linear equations can have?
no solutions
exactly one solution
Infinite solutions
What does consistent mean in linear algebra?
When a system of equations has either only one solution or infinite solutions
What does inconsistent mean in linear algebra?
When a system of linear equations has no solutions
What is a matrix?
When a linear system is written compactly in a rectangle array
What is another word for coefficient matrix?
An augmented matrix
What is a coefficient matrix?
Includes all coefficient in your system, including numbers, not beside x1, x2 and xn
what are the general steps to solve a system of linear equations with four variables in a 4 by-4 format?
- Write the augmented matrix
- Starting from the bottom row, manipulate to get for 0x1+ 0x2+ 0x3+1x4=b and essentially find the value of x4
- substitute value for x4 into equation 3 to find x3 and so on
what is the main gist of solving linear systems?
manipulate the rows to get echelon form
