
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: March 2011
Linear Algebra and Its Applications, Exercise 1.6.9
Exercise 1.6.9. Given the singular matrix show that A has no inverse. If it did have an inverse then multiplying the third row of by the columns of A should give the third row of I. Explain why this is … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.8
Exercise 1.6.8. The matrix has no inverse. Demonstrate this by trying to solve the following: Answer: Multiplying the first row of the first marix by the first column of the second matrix gives However multiplying the second row of the … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.7
Exercise 1.6.7. Find three 2 by 2 matrices A such that and A is neither I nor I. Answer: We first note that the transpose of I is its own inverse: Note that this also follows from the result of … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.6
Exercise 1.6.6. Invert the following matrices using the GaussJordan method: Answer: For the first matrix GaussJordan elimination proceeds as follows: We first subtract 1 times the first row from the second row: This completes the process of forward elimination. We … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.5
Exercise 1.6.5. For a matrix A assume that is invertible and has inverse B. Prove that A is also invertible, with inverse AB. Answer: We have We then have We also have So AB is both a left and right … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.4
Exercise 1.6.4. (a) Given AB = AC, show that B = C if A is invertible. (b) Given find B and C such that AB = AC but . Answer: (a) If A is invertible then (b) If B is … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Exercise 1.6.3
Exercise 1.6.3. Given AB = C, express in terms of B and C. Similar, given PA = LU, express in terms of P, L, and U. Answer: Assume that both B and C are invertible (see below). We then have … Continue reading
Posted in linear algebra
Leave a comment