1 Linear Equations In Linear Algebra Flashcards
A linear system (a system of linear equations):
A collection of one or more linear equations involving the same variable.
Linear equation:
An equation that can be written in the form a1x1 + a2x2 + … + anxn = b where b and the “a” coefficients are real or complex numbers.
Solution (a solution to the system):
A list of numbers that make each equation a true statement when the values are substituted for their respective x.
Solution set:
The set of all possible solutions.
Two linear systems are considered equivalent if…
They have the same solution set.
The solution set is a representation of…
The intersection point of the graphs of the lines.
A solution set can have how many answers?
None, one, or infinitely many
A linear system is consistent if…
It has one or infinitely many solutions.
A system of linear equations is inconsistent if…
It has no solution.
Matrix notation:
The essential information of a linear system.
What does it mean if a matrix is a coefficient matrix (augmented matrix)?
The matrix includes values of b.
Size of a matrix:
Tells how many rows and columns a matrix has in mxn form, where m is the number of rows and n is the columns
What are the elementary row operations?
Replacement, Interchanging, and Scaling
What is the row operation Replacement?
Replace one row by the sum of itself and a multiple of another row.
What is the row operation Interchanging?
Interchange two rows.
