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Tag Archives: linear independence
Linear Algebra and Its Applications, Exercise 3.1.2
Exercise 3.1.2. For give an example of linearly independent vectors that are not mutually orthogonal, as well as mutually orthogonal vectors that are not linearly independent. Answer: The vectors and are linearly independent, since the second vector cannot be expressed … Continue reading
Linear Algebra and Its Applications, Review Exercise 2.33
Review exercise 2.33. Consider the following factorization: a) What is the rank of ? b) Find a basis for the row space of . c) Are rows 1, 2, and 3 of linearly independent: true or false? d) Find a … Continue reading
Posted in linear algebra
Tagged basis, column space, dimension, factorization, general solution, linear independence, nullspace, rank, row space
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Linear Algebra and Its Applications, Review Exercise 2.20
Review exercise 2.20. Consider the set of all 5 by 5 permutation matrices. How many such matrices are there? Are the matrices linearly independent? Do the matrices span the set of all 5 by 5 matrices? Answer: An example member … Continue reading
Posted in linear algebra
Tagged linear independence, permutation matrices, spanning set, subspace
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