# Monthly Archives: September 2011

## Linear Algebra and Its Applications, Exercise 2.3.23

Exercise 2.3.23. Let through be vectors in . Answer the following questions: a) Are the nine vectors linearly independent? Not linearly independent? Might be linearly independent? b) Do the nine vectors span ? Not span ? Might span ? c) … Continue reading

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## Linear Algebra and Its Applications, Exercise 2.3.22

Exercise 2.3.22. Given a vector space of dimension 7 and a subspace of of dimension 4, state whether the following are true or false: 1) You can create a basis for by adding three vectors to any set of vectors … Continue reading

## Linear Algebra and Its Applications, Exercise 2.3.21

Exercise 2.3.21. Suppose is a 64 by 17 matrix and has rank 11. How many independent vectors are solutions to the system ? What about the system ? Answer: If the rank of is 11 then performing elimination on produces … Continue reading

## Linear Algebra and Its Applications, Exercise 2.3.20

Exercise 2.3.20.Consider the set of all 2 by 2 matrices that have the sum of their rows equal to the sum of their columns. What is a basis for this subspace? Consider the analogous set of 3 by 3 matrices … Continue reading

## Linear Algebra and Its Applications, Exercise 2.3.19

Exercise 2.3.19. Suppose is an by matrix, with columns taken from . What is the rank of if its column vectors are linearly independent? What is the rank of if its column vectors span ? What is the rank of … Continue reading