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Chapter 2: Linear Transformations

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Linear Algebra With Applications
Pages: 41 - 109
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Illustration

262 Questions for Chapter 2: Linear Transformations

  1. Find a nonzeron×n matrix Awith identical entries such thatA2=A.

    Found on Page 103

  2. Consider two n x nmatrices A and B whose entries are positive or zero. Suppose that all entries of A are less than or equal to ‘s’, and all column sums of B are less than or equal to ‘r’ (the column sum of a matrix is the sum of all the entries in its column). Show that all entries of the matrix AB are less than or equal to ‘sr’.

    Found on Page 103

  3. Question 103: (This exercise builds on Exercise 49, 101, and 102.)

    Found on Page 104

  4. Found on Page 104

  5. Question 107: Let ℕ be the set of all positive integers, 1, 2, 3,…. We define two functions f and g fromℕ to ℕ:

    Found on Page 105

  6. Question 108:

    Found on Page 105

  7. If possible, compute the matrix products in Exercises 1 through 13, using paper and pencil.

    Found on Page 85

  8. Decide whether the matrices in Exercises 1 through 15 are invertible. If they are, find the inverse. Do the computations with paper and pencil. Show all your work. 10.

    Found on Page 97

  9. Question: Refer to Exercise 10. Find the matrix of the reflection about the lineL.

    Found on Page 71

  10. Matrixis invertible for all real numbers k.

    Found on Page 41

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