Practice Matrix Approach: Row Reduction (23.6) - Linear Independence - Mathematics (Civil Engineering -1)
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Matrix Approach: Row Reduction

Practice - Matrix Approach: Row Reduction

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Determine whether the vectors [1, 2] and [2, 4] are linearly independent.

💡 Hint: Check if one vector can be expressed as a multiple of the other.

Question 2 Easy

Is the set of vectors {[1, 0], [0, 1]} linearly independent?

💡 Hint: Visualize their placement on a graph.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the first step to determine if vectors are linearly independent using a matrix?

A. Check their dot product
B. Form a matrix with them as columns
C. Look for scalar multiples

💡 Hint: Think about the initial setup in matrix terms.

Question 2

True or False: If the number of pivot columns equals the number of vectors, they are dependent.

True
False

💡 Hint: Recall the defining characteristics of dependence.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the vectors A: [1, 2, 3], B: [4, 5, 6], and C: [7, 8, 9], determine if they are independent using row reduction.

💡 Hint: Look for identical rows during reduction.

Challenge 2 Hard

In R^3, analyze the vectors [1, 2, 3], [2, 4, 6], [1, 0, 0]. Is it possible for them to be independent?

💡 Hint: Check whether any vector can be generated from others.

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