Practice Orthonormal Set - 21.9.2 | 21. Linear Algebra | Mathematics (Civil Engineering -1)
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Orthonormal Set

21.9.2 - Orthonormal Set

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Practice Questions

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Question 1 Easy

Define an orthonormal set.

💡 Hint: Think about the definitions of both orthogonal and unit vectors.

Question 2 Easy

What is the dot product of orthogonal vectors?

💡 Hint: Orthogonal means at right angles; what happens when you multiply their components?

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What characterizes an orthonormal set?

Vectors are parallel
Vectors are orthogonal and unit vectors
Vectors have arbitrary lengths

💡 Hint: Think of the definitions of orthogonal and unit.

Question 2

True or False: The Gram-Schmidt process can be used to convert a set of dependent vectors into an orthonormal set.

True
False

💡 Hint: Recall the conditions necessary for applying the Gram-Schmidt process.

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Challenge Problems

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Challenge 1 Hard

Using the vectors v1 = (3, 1) and v2 = (2, 2), apply the Gram-Schmidt process and derive the orthonormal set.

💡 Hint: Start by calculating the lengths and projections step by step.

Challenge 2 Hard

Discuss a scenario in engineering where using an orthonormal set would help in simplifying complex calculations.

💡 Hint: Think about how simplifying computations streamlines structural modeling.

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