Practice Orthogonality And Linear Independence (23.15)

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6 sample questions

Question 1.
Define orthogonality in your own words.
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Think about the geometric interpretation of two lines.
Question 2.
Are the vectors [1, 2] and [-2, 1] orthogonal? Justify your answer.
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Calculate the dot product to check.
3Question 3.
What does it mean for two vectors to be orthogonal?
- They have the same direction
- Their dot product is zero
- They are linearly dependent
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Think about the geometric relationship between the vectors.
4Question 4.
Is it true or false? Orthogonal vectors cannot be linearly dependent.
- True
- False
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Consider the properties of independence!
Question 5.
Given the vectors A = [3, -4], B = [4, 2], and C = [0, 0], determine if they are linearly independent. Provide a justification.
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Calculate dot products and assess the coefficients.
Question 6.
In a mechanical system, explain how having linearly dependent vectors can impact the solution to structural analysis problems.
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Consider the equations in equilibrium and how they relate to the forces in the structure.

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