
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: January 2011
Linear Algebra and Its Applications, Exercise 1.5.19
Exercise 1.5.19. For the following two matrices, specify the values of , , and for which elimination requires row exchanges, and the values for which the matrices in question are singular. Answer: For the first matrix a row exchange would … Continue reading
Posted in linear algebra
2 Comments
Linear Algebra and Its Applications, Exercise 1.5.18
Exercise 1.5.18. We have the following systems of linear equations: and and Which of the systems are singular, and which nonsingular? Which have no solutions? One solution? An infinite number of solutions? Answer: For the first system we can add … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.5.17
Exercise 1.5.17. If LPU order is used then rows are exchanged only at the end of elimination: Specify what L is in the above case. Answer: Since no row exchanges are done during elimination proper, the multipliers in L stay … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.5.16
Exercise 1.5.16. Find a 4 by 4 matrix (preferably a permutation matrix) that is nonsingular and for which elimination requires three row exchanges. Answer: The following permutation matrix meets the requirement: For this matrix elimination requires the following row exchanges: … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.5.15
Exercise 1.5.15. Given the matrices and find their factors L, D, and U and associated permutation matrix P such that PA = LDU. Confirm that the factors are correct. Answer: In the first step in elimination for the first matrix … Continue reading
Posted in linear algebra
9 Comments
Linear Algebra and Its Applications, Exercise 1.5.14
Exercise 1.5.14. Find all possible 3 by 3 permutation matrices, along with their inverses. Answer: The identity matrix I is the first possible permutation matrix, corresponding to not doing a row exchange at all; it is its own inverse: The … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.5.13
Exercise 1.5.13. Given the systems of equations and solve both by elimination. Do row exchanges where necessary, and specify any permutation matrices required. Answer: The first system of equations can be expressed as follows: In the first step of elimination … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.5.12
Exercise 1.5.12. Could be factored into the product where is upper triangular and is lower triangular, instead of being factored into the product ? If so, how could this other factorization be carried out? Would and be the same in … Continue reading
Posted in linear algebra
Tagged factorization, lower triangular matrix, upper triangular matrix
4 Comments
Linear Algebra and Its Applications, Exercise 1.5.11
Exercise 1.5.11. We have a system LUx = b with values for L, U, and b as follows: Solve for x without multiplying L and U to find A. Answer: We can take advantage of the equations Lc = b … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.5.10
Exercise 1.5.10. (a) Both Lc = b and Ux = c take approximately multiplicationsubstraction steps to solve. Explain why. (b) Assume A is a 60 by 60 coefficient matrix. How many steps are required to use elimination to solve ten … Continue reading
Posted in linear algebra
Leave a comment