21.7.2 - Use in Engineering
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Practice Questions
Test your understanding with targeted questions
Define linear dependence.
💡 Hint: Think of whether one vector can be formed with the others.
What is linear independence?
💡 Hint: Remember, the scalars must all be zero.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines linear dependence?
💡 Hint: Think about how vectors relate to each other.
True or False: The vector set { (1, 2), (2, 4) } is linearly independent.
💡 Hint: Check if one vector can be made by combining others.
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Challenge Problems
Push your limits with advanced challenges
Consider the vectors v1 = (1, 2, 3), v2 = (2, 4, 6), and v3 = (3, 6, 9). Are these vectors linearly dependent or independent? Justify your answer.
💡 Hint: Look for constants that can express one vector through another.
An engineer decides to remove redundant structural supports based on vector analysis. If the original supports were based on vectors that are dependent, how would this affect the safety of the structure?
💡 Hint: Re-evaluate the role each support plays in load-bearing.
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