Practice Linear Independence (24.5) - Vector Space - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Identify if the vectors (1, 2) and (3, 6) are independent or dependent.
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Look for scalar multiples.
Question 2.
Are the vectors (2,1) and (1,-2) independent?
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Check if you can express one in terms of the other.
3Question 3.
What characterizes a set of linearly independent vectors?
- They can form the zero vector only with zero coefficients
- They can be expressed as linear combinations of others
- They span the entire vector space
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Think about what it means for vectors to combine to zero.
4Question 4.
True or False: The vectors (1, 2) and (2, 4) are linearly independent.
- True
- False
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Check if one vector is a multiplier of the other.
Question 5.
Prove that the vectors (2, 3) and (2, 6) are dependent by showing a scalar relationship.
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Form a linear combination to see if you can make zero.
Question 6.
Given vectors (3, 1) and (1, 3), find a linear combination that shows they are independent or dependent.
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Try setting up the equation with scalars to see if it leads to a solution.

4 more questions in this section. Enroll free to practise them all.