Practice Linear Independence - 23 | 23. Linear Independence | Mathematics (Civil Engineering -1)
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Linear Independence

23 - Linear Independence

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Determine if the following vectors are linearly independent: [1, 2], [2, 3].

💡 Hint: Try forming a linear equation with both vectors.

Question 2 Easy

Are the vectors [1, 0] and [0, 1] linearly independent?

💡 Hint: Think about spanning a plane.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

A set of vectors is linearly independent if:

At least one vector can be expressed as a linear combination of others
The only solution to their linear combination equaling zero is non-trivial
The only solution to their linear combination equaling zero is trivial

💡 Hint: Recall what a trivial solution is.

Question 2

If a set of vectors are collinear in R^2, are they linearly independent?

True
False

💡 Hint: Think about spanning a plane.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Show that the vectors [1, 0, 0], [0, 1, 0], [0, 0, 1] form a basis for R^3.

💡 Hint: Check for linear combinations.

Challenge 2 Hard

Given vectors in R^3, [x, 2x, 3x], under what conditions for 'x' are they dependent?

💡 Hint: Consider the implications of scalar multiples.

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