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5: Let F: VW be a linear mapping, where the vector space V has dimension 5 and the vector space W has dimension 7. Which of the following is true? A) The matrix F does not depend on the choice of base y for V and w for W, i.e. we get the same matrix no matter which bases we choose. B) The matrix F depends on the bases we choose, but is always a 7 × 5-matrix C) The matrix F depends on the choice of base, and the number of rows and columns in the matrix also depends on the choice of base.

5: Let F: VW be a linear mapping, where the vector space V has dimension 5 and the vector space W has dimension 7. Which of the following is true? A) The matrix F does not depend on the choice of base y for V and w for W, i.e. we get the same matrix no matter which bases we choose. B) The matrix F depends on the bases we choose, but is always a 7 × 5-matrix C) The matrix F depends on the choice of base, and the number of rows and columns in the matrix also depends on the choice of base.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5: Let F: VW be a linear mapping, where the vector space V has dimension 5 and the vector space W has dimension 7. Which of the following is true? A) The matrix F does not depend on the choice of base y for V and w for W, i.e. we get the same matrix no matter which bases we choose. B) The matrix F depends on the bases we choose, but is always a 7 × 5-matrix C) The matrix F depends on the choice of base, and the number of rows and columns in the matrix also depends on the choice of base.
Transcribed Image Text:5: Let F: VW be a linear mapping, where the vector space V has dimension 5 and the vector space W has dimension 7. Which of the following is true? A) The matrix F does not depend on the choice of base y for V and w for W, i.e. we get the same matrix no matter which bases we choose. B) The matrix F depends on the bases we choose, but is always a 7 × 5-matrix C) The matrix F depends on the choice of base, and the number of rows and columns in the matrix also depends on the choice of base.
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