# Tag Archives: nullspace

## Linear Algebra and Its Applications, Exercise 3.3.20

Exercise 3.3.20. Given the matrix that projects onto the row space of , find the matrix that projects onto the nullspace of . Answer: The null space of is orthogonal to the row space of . The two spaces are orthogonal complements, with … Continue reading

## Linear Algebra and Its Applications, Exercise 3.1.15

Exercise 3.1.15. Is there a matrix such that the vector is in the row space of the matrix and the vector is in the nullspace of the matrix? Answer: The row space of any matrix is the orthogonal complement to … Continue reading

## Linear Algebra and Its Applications, Exercise 3.1.12

Exercise 3.1.12. For the matrix find a basis for the nullspace and show that it is orthogonal to the row space. Take the vector and express it as the sum of a nullspace component and a row space component . … 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

## 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 2.30

Review exercise 2.30. Suppose that the matrix is a square matrix. a) Show that the nullspace of contains the nullspace of . b) Show that the column space of contains the column space of . Answer: a) Suppose is in … Continue reading