Tag Archives: linear transformation

Linear Algebra and Its Applications, Review Exercise 2.29

Posted on January 11, 2014 by hecker

Review exercise 2.29. The following matrices represent linear transformations in the – plane with and as a basis. Describe the effect of each transformation. Answer: When the matrix is applied to the vector we obtain When the matrix is applied … Continue reading →

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Linear Algebra and Its Applications, Review Exercise 2.26

Posted on December 29, 2013 by hecker

Review exercise 2.26. State whether the following statements are true or false: a) For every subspace of there exists a matrix for which the nullspace of is . b) For any matrix , if both and its transpose have the … Continue reading →

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Linear Algebra and Its Applications, Review Exercise 2.25

Posted on December 28, 2013 by hecker

Review exercise 2.25. Suppose that is a linear transformation from to itself, and transforms the point to the point . What does the inverse transformation do to the point ? Answer: The effect of is to reverse the effect of … Continue reading →

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Linear Algebra and Its Applications, Review Exercise 2.23

Posted on December 21, 2013 by hecker

Review exercise 2.23. Given any three vectors , , and in find a matrix that transforms the three elementary vectors , , and respectively into those three vectors. Answer: When multiplying by only the entries in the first column of … Continue reading →

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