Tag Archives: rank

Linear Algebra and Its Applications, Exercise 3.3.8

Exercise 3.3.8.¬†Suppose that is a projection matrix from onto a subspace with dimension . What is the column space of ? What is its rank? Answer: Suppose that is a arbitrary vector in . From the definition of we know … Continue reading

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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

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Linear Algebra and Its Applications, Review Exercise 2.28

Review exercise 2.28. a) If is an by matrix with linearly independent rows, what is the rank of ? The column space of ? The left null space of ? b) If is an 8 by 10 matrix and the … Continue reading

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Linear Algebra and Its Applications, Review Exercise 2.22

Review exercise 2.22. a) Given what conditions must satisfy in order for to have a solution? b) Find a basis for the nullspace of . c) Find the general solution for for those cases when a solution exists. d) Find … Continue reading

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Linear Algebra and Its Applications, Review Exercise 2.21

Review exercise 2.21. Consider an by matrix with the value 1 for every entry. What is the rank of such a matrix? Consider another by matrix equivalent to a checkerboard, with if is even and if is odd. What is … Continue reading

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Linear Algebra and Its Applications, Exercise 2.2.3

Exercise 2.2.3. Consider the system of linear equations represented by the following matrix: Find the factorization , a set of basic variables, a set of free variables, a general solution to (expressed as a linear combination as in equation (1) … Continue reading

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