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Tutorial Math 204 Tutorial 1 System of linear equations Gauss / Gauss - Jordan reduction
by Rogelio Yoyontzin
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Tutorial Math 204 Tutorial 1 System of linear equations Gauss / Gauss - Jordan reduction

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Problem 1

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Find the augmented matrix of the system

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Gauss/Gauss Jordan Reduction

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The system with zeros

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Reduce echalon form

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Is this the best way to solve it?

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Probelm 2 to be solved in the blackboard

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Problem 3 to be solved in the Blackboard by students

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Problem 4

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Important Points To Remark

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How to write the steps in the Aug.Coeff.Matrix(ACM). Write the ACM and beside it state the Elementary Row Operation(ERO) to be executed.

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What happens when a 1 cannot be determined on a row?

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Start at the bottom of the final ACM when interpreting the final solution.

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How the General solution is to be written with parameters and also a couple of particular solutions

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how to avoid fractions until the last ERO is to be done. You do not have to get the ones first. Get the zeros first if it helps to avoid fractions (see 5c in notes)

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First Find The Augmented Matrix of the following examples:

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Ph. D Candiate: Jesús Rogelio Pérez Buendía. If you want to send me an email please use Moodle email service. You can Find me on The Math Help Centre LB 912. You will hae acces to this matherial on Moodle Meta Site. You will have a 15 min Quiz based on one (similar) exercise on this asignment and/or Tutorial problems for next week.

Specifically, a matrix is in row echelon form if All nonzero rows (rows with at least one nonzero element) are above any rows of all zeroes (all zero rows, if any, belong at the bottom of the matrix). The leading coefficient (the first nonzero number from the left, also called the pivot) of a nonzero row is always strictly to the right of the leading coefficient of the row above it. All entries in a column below a leading entry are zeroes (implied by the first two criteria).[1] Some texts add the condition that the leading coefficient of any nonzero row must be 1.[2]