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Tag Archives: column space
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 2.32
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
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
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
Linear Algebra and Its Applications, Review Exercise 2.24
Review exercise 2.24. Suppose that is a 3 by 5 matrix with the elementary vectors , , and in its column space. Does has a left inverse? A right inverse? Answer: Since , , and are in the column space … Continue reading
Posted in linear algebra
Tagged column space, elementary vectors, left inverse, right inverse
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Linear Algebra and Its Applications, Review Exercise 2.8
Review exercise 2.8. Do the following: a) Find a matrix whose nullspace contains the vector . b) Find a matrix whose left nullspace contains the vector . c) Find a matrix with column space spanned by and row space spanned … Continue reading
Posted in linear algebra
Tagged column space, left nullspace, nullspace, row space, spanning set
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