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Math 221 Class Notes 05-15-13.docx

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MATH 221
Alexandra Pettet

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Math 221 May 15 2013 Alexandra Pettet Html Office Location: Math 229F Office Hours: Wed 2—4 PM Thu 12 noon—1 PM Linear Systems ° Encode into matrix system  Constants / Co-efficients ° Row operations to matrix system  Operations to linear system ° Simplify matrix to get solution set Row operations 1. Add a multiple of a row to another row 2. Interchange two rows 3. Multiplying a row by a nonzero scalar Two matrices are row equivalent if one can be obtained from the other b a sequence of row operations General Strategy for solving a linear system 1. Encode the system into an augmented matrix 2. Use row operations to put the matrix into a simpler form 3. Read off the solution from Step 2 Systematic way of solving a linear system What do we mean by a “simpler form” in Step 2 A matrix is in a (row) echelon form (echelon: steplike) if it has the following properties 1. All rows with a nonzero entry are above rows, all of whose entries are zero 2. The leading entry (or pivot) of a row is its first nonzero entry. Each leading entry is in a column to the right o
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