Monthly Archives: August 2012

Exercise 2.4.20. For each of the following properties find a matrix with that property. If no such matrix exists, explain why that is the case. a) The column space of the matrix contains the vectors and the row space contains … Continue reading →

Exercise 2.4.19. For the following matrix find a basis for each of the four associated subspaces. Answer: Per the above equation the matrix on the left side can be factored into a lower triangular matrix with unit diagonal and an … Continue reading →

Exercise 2.4.18. Given the vectors and the subspace that they span, find two matrices and such that . Answer: The easiest way to create a matrix whose row space is is to use the vectors above as the rows of … Continue reading →

Exercise 2.4.17. Point out the error in the following argument: Suppose is a right-inverse of so that . Then we can multiply both sides by to produce or . But we then have so that is a left-inverse as well. … Continue reading →