
Archives
 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
Monthly Archives: May 2011
Linear Algebra and Its Applications, Exercise 1.6.18
Exercise 1.6.18. Suppose that Show that Answer: We have The product of two upper triangular matrices is also an upper triangular matrix, and multiplying by a diagonal matrix preserves this. The left side of the final equation above is therefore … Continue reading
Posted in linear algebra
Leave a comment
Linear Alegbra and Its Applications, Exercise 1.6.17
Exercise 1.6.17. (a) Suppose that the n by n matrix A can be factored as LDU, where L and U have ones on the diagonal. Factor the transpose of A. (b) If we have what triangular systems will provide a … Continue reading
Posted in Uncategorized
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.16
Exercise 1.6.16. (i) If A is an n by n symmetric matrix, how many entries of A can be chosen independently of each other? (ii) If If K is an n by n skewsymmetric matrix, how many entries of K … Continue reading
Posted in linear algebra
2 Comments
Linear Algebra and Its Applications, Exercise 1.16.15
Exercise 1.6.15. For any square matrix B and matrices A and K where prove that A is symmetric and K is skewsymmetric, i.e., For the case where compute A and K and show that B can be expressed as the … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.14
Exercise 1.6.14. For any m x n matrix A, prove that and are symmetric matrices. Provide an example where these matrices are not equal. Answer: Per Equation 1M(i) on page 47 we have Substituting for B we have Since is … Continue reading
Posted in Uncategorized
Leave a comment
Linear Algebra and Its Applications, Exercise 1.16.13
Exercise 1.6.13. Compute , , , and for the following matrices: Answer: We have Note that per Equation 1M(i) on page 47 we have This means that and as confirmed by the computation above. NOTE: This continues a series of … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.12
Exercise 1.6.12. Suppose that A is an invertible matrix and has one of the following properties: (1) A is a triangular matrix. (2) A is a symmetric matrix. (3) A is a tridiagonal matrix. (4) All the entries of A … Continue reading
Posted in linear algebra
Leave a comment