
Archives
 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: rank
Linear Algebra and Its Applications, Exercise 3.3.8
Exercise 3.3.8. Suppose that is a projection matrix from onto a subspace with dimension . What is the column space of ? What is its rank? Answer: Suppose that is a arbitrary vector in . From the definition of we know … 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 2.28
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 2.22
Review exercise 2.22. a) Given what conditions must satisfy in order for to have a solution? b) Find a basis for the nullspace of . c) Find the general solution for for those cases when a solution exists. d) Find … Continue reading
Posted in linear algebra
Tagged basis of column space, basis of nullspace, conditions on b, general solution, rank
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.21
Review exercise 2.21. Consider an by matrix with the value 1 for every entry. What is the rank of such a matrix? Consider another by matrix equivalent to a checkerboard, with if is even and if is odd. What is … Continue reading
Linear Algebra and Its Applications, Exercise 2.2.3
Exercise 2.2.3. Consider the system of linear equations represented by the following matrix: Find the factorization , a set of basic variables, a set of free variables, a general solution to (expressed as a linear combination as in equation (1) … Continue reading