
Archives
 October 2021
 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: November 2013
Linear Algebra and Its Applications, Review Exercise 2.17
Review exercise 2.17. Suppose that is a vector in and that for all . Show that must be the zero vector. Answer: For and we have SinceĀ for all we must have for each of the elementary vectors , , … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.16
Review exercise 2.16. For each of the cases in review exercise 2.15, describe the relationship among the rank of , the number of rows , and the number of columns . Answer: (i) For the matrix we have , , … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.15
Review exercise 2.15. For each of the following, find a matrix for which i) there is either no solution or one solution to depending on ii) there are an infinite number of solutions to for all iii) there is either … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.14
Review exercise 2.14. Do the three vectors , , and form a basis for the vector space ? Answer: In order for the three vectors to be a basis for they must be linearly independent. We can test this by … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.13
Review exercise 2.13. For the matrix find its triangular factors and describe the conditions under which the columns of are linearly independent. Answer: We start elimination by subtracting 1 times the first row from the second row, with We next … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.12
Review exercise 2.12. The matrix is by and has rank . What is the dimension of its nullspace? Answer: The dimension of the nullspace is the number of columns of minus the rank of , or . NOTE: This continues … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.11
Review exercise 2.11. a) Given the following matrix find its rank and a basis for the nullspace. b) Are the first three rows of a basis for the row space of ? Are the first, third, and sixth columns of … Continue reading
Posted in linear algebra
Leave a comment
Linear Algebra and Its Applications, Review Exercise 2.10
Review exercise 2.10. Given the set of all linear transformations from to define operations for scalar multiplication and vector addition that will make the set a vector space. What is the dimension of the resulting vector space? Answer: Let and … Continue reading
Posted in linear algebra
2 Comments
Linear Algebra and Its Applications, Review Exercise 2.9
Review exercise 2.9. Answer the following questions for the vector space of 2 by 2 matrices: a) Does the set of 2 by 2 matrices with rank 1 form a subspace? b) What is the subspace spanned by the 2 … Continue reading
Posted in linear algebra
Tagged invertible matrices, permutation matrices, positive matrices, spanning set, subspace
Leave a comment