-
Archives
- October 2021
- January 2021
- March 2019
- January 2018
- December 2017
- January 2017
- December 2016
- November 2016
- October 2016
- September 2016
- July 2016
- October 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- March 2013
- February 2013
- January 2013
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- April 2012
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- January 2011
- August 2010
- June 2010
- May 2010
- November 2009
-
Meta
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
Posted in linear algebra
Tagged basis, nullspace, nullspace component, row space component
Leave a comment
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
Leave a comment
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 2.8
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
Leave a comment
My Math Homework 