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## Matrix Map

by: Marina Camacho

4

1

1

# Matrix Map MA371

Marina Camacho

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The matrix map attached explains a table in which a matrix can be classified under different descriptions (i.e. onto, unique, non-homogeneous, homogeneous, one to one, independent). The flow diagra...
COURSE
Linear Algebra
PROF.
TYPE
Class Notes
PAGES
1
WORDS
CONCEPTS
Linear Algebra, Systems, Engineering, Calculus, Math, Matrices, Matrix
KARMA
25 ?

## Popular in Mathematics

This 1 page Class Notes was uploaded by Marina Camacho on Monday September 12, 2016. The Class Notes belongs to MA371 at United States Military Academy taught by in Fall 2016. Since its upload, it has received 4 views. For similar materials see Linear Algebra in Mathematics at United States Military Academy.

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Date Created: 09/12/16
MA371: Linear algebra So, you have a matrix… START Is the matrix consistent (1 unique or infinite solution) or inconsistent (no solution)? Inconsistent: Consistent: Consistent: the No Solution The solution is only solution is (All Zeros in unique or the zero vector Last column infinite and/or (Lesson 2). of contains a free variable Matrix (Lesson 2). correspondin g “Non-Trivial Solution” “Trivial Solution”  Contains a solution other than the  Trivial solution: Always has 1  trivial solution, unique or a free  solution (Ax = 0) (Lesson 5). variable (Lesson 5).  Homogenous Solution: Ax=0 has a  Non-homogenous solution: May  nontrivial solution if and only if the  contain a free variable or unique solution equation has at least one free variable  (Lesson 5).  (Lesson 5).  Linear dependence: Contains free   Linear independence: Only has  variable, may or may not have a pivot in  trivial solution, must have a pivot in  each row or a unique solution (Lesson  each row, and no free variables (Lesson  6).  6).    Transformation: Onto: A mapping   (Theorem 11) Transformation: T: Rn → Rm is ONTO Rm if b€Rm is  one to one: A mapping T: Rn → Rm  the image of at least one x€Rn (Lesson  is One to one if an only if this  8).  transformation T(x)=0 has only the  trivial solution x=0 (vector) (Lesson 8).

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