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Tag Archives: basis
Linear Algebra and Its Applications, Exercise 3.3.12
Exercise 3.3.12. Given the subspace spanned by the two vectors and find the following: a) a set of basis vectors for b) the matrix that projects onto c) the vector in that has the minimum distance to the vector in Answer: … Continue reading
Posted in linear algebra
Tagged basis, column space, left nullspace, orthogonal complement, projection matrix
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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
Posted in linear algebra
Tagged basis, nullspace, nullspace component, row space component
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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
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, Exercise 2.4.3
Exercise 2.4.3. For each of the two matrices below give the dimension and find a basis for each of their four subspaces: Answer: We first consider the column spaces and . The matrix has two pivots and therefore rank ; … Continue reading
Linear Algebra and Its Applications, Exercise 2.4.2
Exercise 2.4.2. For each of the two matrices below give the dimension and find a basis for each of their four subspaces: Answer: The echelon matrix has only a single pivot, in the second column. As discussed on page 93, … Continue reading