25.10.1 - Gaussian Elimination
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Practice Questions
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What is the first step in the Gaussian elimination process?
💡 Hint: Think about how we prepare the matrix for substitution.
List one type of row operation used in Gaussian elimination.
💡 Hint: What operations can change the arrangement of matrix rows?
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Interactive Quizzes
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What is the final step in Gaussian elimination?
💡 Hint: What do you do after transforming the matrix into upper triangular form?
True or False: Gaussian elimination can be used to solve any system of linear equations.
💡 Hint: Is there a reason it wouldn't apply?
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Challenge Problems
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Solve the following system using Gaussian elimination: \[\begin{align} x + 2y + 3z &= 9 \ 2x + 3y + z &= 8 \ 3x + y + 2z &= 7 \end{align}\]
💡 Hint: Modify each equation until zeros are created beneath pivots.
A matrix represents a system where Gaussian elimination leads to a row of zeros. What conclusions can you draw about the solution's nature?
💡 Hint: Investigate if the equations remain true even with one row eliminated.
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