Tag Archives: subspace

Linear Algebra and Its Applications, Exercise 3.3.9

Exercise 3.3.9.¬†Suppose that is a¬†matrix such that . a) Show that is a projection matrix. b) If then what is the subspace onto which projects? Answer: a) To show that is a projection matrix we must show that and also … Continue reading

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Linear Algebra and Its Applications, Review Exercise 2.32

Review exercise 2.32. a) Find the subspace of such that for any vector in the subspace we have . b) Find a matrix for which this subspace is the nullspace. c) Find a matrix for which this subspace is the … Continue reading

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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

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Linear Algebra and Its Applications, Review Exercise 2.9

Review exercise 2.9. Answer the following questions for the vector space of 2 by 2 matrices: a) Does the set of 2 by 2 matrices with rank 1 form a subspace? b) What is the subspace spanned by the 2 … Continue reading

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