
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
Monthly Archives: December 2013
Linear Algebra and Its Applications, Review Exercise 2.26
Review exercise 2.26. State whether the following statements are true or false: a) For every subspace of there exists a matrix for which the nullspace of is . b) For any matrix , if both and its transpose have the … Continue reading
Linear Algebra and Its Applications, Review Exercise 2.25
Review exercise 2.25. Suppose that is a linear transformation from to itself, and transforms the point to the point . What does the inverse transformation do to the point ? Answer: The effect of is to reverse the effect of … 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
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.23
Review exercise 2.23. Given any three vectors , , and in find a matrix that transforms the three elementary vectors , , and respectively into those three vectors. Answer: When multiplying by only the entries in the first column of … Continue reading
Posted in linear algebra
Tagged elementary vectors, invertible, linear transformation
Leave a comment
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, Review Exercise 2.20
Review exercise 2.20. Consider the set of all 5 by 5 permutation matrices. How many such matrices are there? Are the matrices linearly independent? Do the matrices span the set of all 5 by 5 matrices? Answer: An example member … Continue reading
Posted in linear algebra
Tagged linear independence, permutation matrices, spanning set, subspace
Leave a comment