
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: row space
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 3.3.19
Exercise 3.3.19. Given a matrix , the matrix projects onto the column space of . Find the matrix that projects onto the row space of . Answer: The row space of is the column space of . We can then … 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 3.1.13
Exercise 3.1.13. Provide a picture showing the action of in sending the column space of to the row space and the left nullspace to zero. Answer: I’m leaving this post as a placeholder until I have time to illustrate this. … Continue reading
Linear Algebra and Its Applications, Exercise 3.1.7
Exercise 3.1.7. For the matrix find vectors and such that is orthogonal to the row space of and is orthogonal to the column space of > Answer: The nullspace of is orthogonal to the row space of . We can … 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
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 2.8
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