Arturo O. answered • 07/27/18

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Here is a counterexample to show it is false.

X

_{1}= (1, 0, 0)X

_{2}= (0, 1, 0)X

_{3}= (0, 2, 0)X

_{1}and X_{2}are linearly independent.X

_{1}and X_{3}are linearly independent.But X

_{2}is not linearly independent of X_{3}, so {X_{1},X_{2},X_{3}} is not a linearly independent set.