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(d) Use the matrix in part (c) to compute  .

Let V be a four-dimensional vector space with basis B, let W be a seven-dimensional vector space

20. with basis , and let                   be a linear transformation. Identify the four vector spaces that

contain the vectors at the corners of the accompanying diagram.

                                                                            Figure Ex-20
                                  In each part, fill in the missing part of the equation.
                             21.

                                      (a)

                                      (b)

                                  Give two reasons why matrices for general linear transformations are important.
                             22.

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