Fundamentals of Engineering Analysis

1
Fundamentals of Engineering Analysis EGR 1302
Unit 1, Lecture F Approximate Running Time - 24
minutes Distance Learning / Online Instructional
Presentation Presented by Department of
Mechanical Engineering Baylor University

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2
Solving Systems of Linear Equations
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Solution by Cramers Rule
Cramers Rule is only valid for Unique
Solutions. If detA 0, Cramers Rule fails!
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Solve a System of Equations with Cramers Rule
Remember ratio of determinants
5
The Need for a General Solution to Linear Systems
Cramers Rule is only valid for Unique
Solutions. If detA 0, Cramers Rule fails!
We need a method of finding a general
solution when the coefficient matrix A is
Singular.
6
Gaussian Elimination - A general solution
Methodology
We will use three elementary row operations to
solve this set of linear equations by Gaussian
Elimination.
7
Using Elementary Row Operations to Solve by
Gaussian Elimination
1. Keep Row 1 the same
2. Keep Row 2 the same
Step 3 Use Rule 1 to reduce all coefficients to
1
1. Keep Row 1 the same
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The Augmented Matrix
augmented matrix
can be represented as
Row Echelon Form
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Reduced Row Echelon Form of the Augmented Matrix
Using Backwards Substitution on the Row Echelon
Form
10
Using the TI-89 to do Gaussian Elimination
Note that calculator computes a different REF
result, by using a different algorithm, but the
answer is still correct.
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This concludes Unit 1, Lecture F