Practice Examples (23.7) - Linear Independence - Mathematics (Civil Engineering -1)

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6 sample questions

Question 1.
Are the vectors [2, 1], [4, 2] linearly independent?
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Check if one vector can be expressed as a scalar multiple of another.
Question 2.
Is the set {(1, 0), (0, 1)} linearly independent?
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Consider the geometric representation of these vectors.
3Question 3.
If a set of three vectors in R3 is dependent, what can be said about their relationships?
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Recall the definitions of linear independence and dependence.
4Question 4.
Is the following statement true or false? 'Three vectors can be linearly independent in a 2-D space.'
- True
- False
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Consider the dimensionality of the space.
Question 5.
Given the vectors [2, 3, 1], [4, 6, 2], [5, 7, 4], determine if they are linearly independent or dependent and explain your reasoning.
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Form a matrix and use row reduction.
Question 6.
Using the vectors (1, 2, -1), (2, 4, 2), (3, 6, 3), show they are dependent and find the relationship between them.
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Look for a common scalar that relates the vectors.

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