Linear Algebra Definitions

The flashcards below were created by user DrGirlfriend on FreezingBlue Flashcards.

1. Algebra
Arabic, "al-jabr"

completion and balancing
2. Linear
"line"

introduces a geometric component
3. Geometry
Earth + Measure
4. Elementary Row Operations
1.) Interchange Rows

2.) Add a multiple of one row to another

3.) Scale a row by a nonzer0 factor
5. Polynomial
sum of many monomials

- degree is highest exponent

-degree one is linear
6. Free Variables
Columns without leading 1's

- if consistent, has many solutions
7. Pivot Variables/Leading Variables/Basic Variables

- where to start when reducing rows
8. Pivot Column
Has a leading 1
9. Pivot Position
used to eliminate nonzero numbers

-same positions in first and last matrices (even if different numbers)
10. Row Reduction
• Algorithm
• Procedure

• - start with a matrix, end with a solution set
• - "Gaussian Elimination"
11. Row Echelon Form
Get leading 1's in all the rows
12. Reduced Row Echelon Form
a.) Nonzero rows above zero rows

b.) Leading entries in higher rows is to the right

c.) All entries below a leading entry are zero

d.) Leading entries in nonzero rows are 1's

e.) All entries above a leading entry are 0
13. Augmented Matrix
Matrix with "equal's" column

- RHS and LHS
14. Coefficient Matrix
Only has coefficients of variables

-LHS

- doesn't include "equal's" column

- in a real-life situations, coefficients won't change, but numbers in the equal's column might.
15. Consistent
has at least one solution

(can have infinitely many solutions)
16. Inconsistent
no solution

(like with parallel lines)
17. Existence and Uniqueness of solutions

How does RREF reflect existence and uniqueness of solutions?
• Existence:
• - 0 =/ 1
•       >no solution exists
•       > Inconsistent
• - free variables
•       > infinitely many solutions exist

• Uniqueness:
• - no free variables means solution is unique
18. Row Equivalence
can go from one to another with row operations
19. Solving a System
determine consistency, then find parameters
20. Overdetermined
More equations than variables

doesn't tell us much
21. Underdetermined
More variables than equations

• - if there are solutions, there are infinitely many
•      > free variables
 Author: DrGirlfriend ID: 193659 Card Set: Linear Algebra Definitions Updated: 2013-01-19 01:08:21 Tags: Linear Algebra Definitions Folders: Description: Sections 1.1 through 1.3 Show Answers: