# Monthly Archives: June 2012

## Linear Algebra and Its Applications, Exercise 2.4.11

Exercise 2.4.11. Suppose that for a matrix and any the system always has at least one solution. Show that in this case the system has no solution other than . Answer: Suppose is an by matrix and is an -element … Continue reading

## Linear Algebra and Its Applications, Exercise 2.4.10

Exercise 2.4.10. Suppose the nullspace of a matrix is the set of all vectors in for which . Find a 1 by 3 matrix with this nullspace. Find a 3 by 3 matrix with the same nullspace. Answer: If and … Continue reading

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## Linear Algebra and Its Applications, Exercise 2.4.9

Exercise 2.4.9. Let be a matrix representing a system of equations in unknowns, and assume that the only solution to is 0. What is the rank of ? Explain your answer. Answer: is a linear combination of the columns of … Continue reading

## Linear Algebra and Its Applications, Exercise 2.4.8

Exercise 2.4.8. Is it possible for the row space and nullspace of a matrix to both contain the vector ? If not, why not? Answer: Suppose is an by 3 matrix and is in the nullspace . Then we must … Continue reading