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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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