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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the first step in the Gram-Schmidt process?
💡 Hint: Think about the length of a vector.
Question 2
Easy
Define orthonormal vectors.
💡 Hint: What properties do the vectors have?
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the Gram-Schmidt process achieve?
- Creates linearly dependent vectors
- Finds a set of orthonormal vectors
- Normalizes a single vector
💡 Hint: Consider what is produced by the process.
Question 2
True or False: The Gram-Schmidt process can only be applied to vectors in \(\mathbb{R}^3\).
- True
- False
💡 Hint: Think about vectors in other spaces too.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the vectors \(v_1 = (2, -1, 1)\) and \(v_2 = (1, 3, -2)\), apply the Gram-Schmidt process to create the orthonormal basis.
💡 Hint: Break down the steps: normalization, projection, and adjust.
Question 2
Using the orthonormal basis computed from previous vectors, solve for the coefficients of a given vector \(w = (0, 0, 1)\) in that basis.
💡 Hint: Remember, the coefficients will tell how much of each unit vector is present.
Challenge and get performance evaluation