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independent set.
Remark The converse of Theorem 5.3.4 is false. If the Wronskian of is identically zero on , then no
conclusion can be reached about the linear independence of
linearly dependent. ; this set of vectors may be linearly independent or
Exercise Set 5.3
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Explain why the following are linearly dependent sets of vectors. (Solve this problem by inspection.)
1.
(a) and in
(b) , , in
(c) and in
(d) and in
Which of the following sets of vectors in are linearly dependent?
2.
(a)
(b)
(c)
(d)
Which of the following sets of vectors in are linearly dependent?
3.
(a)
(b)
