Problem 38
Question
Describe what happens when Gaussian elimination is used to solve a system with dependent equations.
Step-by-Step Solution
Verified Answer
When Gaussian elimination is used to solve a system with dependent equations, during the process of row reduction, a zero row is obtained in the resultant augmented matrix. This indicates the presence of an infinite number of solutions, characteristic of dependent systems.
1Step 1: Understand dependent systems
Dependent systems of equations have infinitely many solutions. For such systems, there are either the same equations or an equation that is a multiple of another, which makes them dependent.
2Step 2: Performing Gaussian elimination
When you start performing Gaussian elimination on a dependent system, you would get a row of zeros in your augmented matrix during row reduction.
3Step 3: Interpretation
The row of zeros is indicating that the equations are identical or one is a multiple of the other, meaning they are dependent. Hence, there is an infinite number of solutions, which is what we expected from a dependent system.
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Problem 38
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