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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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