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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Determine whether the vectors v₁ = [1] and v₂ = [2] are linearly independent.
💡 Hint: Think about whether one can be written as a multiple of the other.
Question 2
Easy
What is meant by 'linear combination'?
💡 Hint: Look at the format: a₁*v₁ + a₂*v₂ + ... + aₙ*vₙ.
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 is a linear combination?
- A sum of vector magnitudes
- A combined vector formed using scalars
- A geometric shape
💡 Hint: Remember its definition involving scalar multiplication.
Question 2
True or False: If a set of vectors is linearly independent, at least one vector can be expressed as a combination of the others.
- True
- False
💡 Hint: Think about the implication of independence.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given three vectors, v₁ = [1, 2, 3], v₂ = [2, 4, 6], and v₃ = [3, 6, 9], show they are linearly dependent using row reduction.
💡 Hint: Check for redundancy in your elimination steps.
Question 2
For the vectors v₁ = [1, 1], v₂ = [a, a] where a is a scalar, find values of a for which the vectors are linearly independent.
💡 Hint: Set the coefficients of the linear combination equal to zero and solve.
Challenge and get performance evaluation