21.9.3 - Gram-Schmidt Process
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Practice Questions
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Define orthogonal vectors.
💡 Hint: Think about the angle between them.
What does it mean for a set of vectors to be orthonormal?
💡 Hint: One condition is that they shouldn't influence each other, and another is that their length should be one.
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Interactive Quizzes
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What does it mean for two vectors to be orthogonal?
💡 Hint: Think about how you can prove two vectors don't affect each other directionally.
True or False? The Gram-Schmidt process can only be applied to vectors in R^3.
💡 Hint: Consider the definition of the process and its universality.
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Challenge Problems
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Given the vectors v1 = (3, 1) and v2 = (2, 2), apply the Gram-Schmidt Process to create an orthonormal set.
💡 Hint: Remember the steps of normalization and projection for each vector.
Explain the importance of using orthonormal vectors in stability analyses in civil engineering.
💡 Hint: Think about how simpler calculations lead to more reliable models in engineering contexts.
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