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4.3: Linear Independence in Vector Spaces 111
9. The union of two linearly independent subsets of a vector
space is linearly independent: true or false?
10. If {u, v}, {v, w}and{w,u} are linearly independent sub-
sets of a vector space, is the subset {u, v, w} necessarily lin-
early independent?
2
11. Show that two non-zero vectors in R are linearly de-
pendent precisely when they are represented by parallel line
segments in the plane.
