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Unformatted text preview: is independent unless u = 0, but if u = 0 is dependent. 3. Suppose 1 2 a. If 1 is linearly dependent, 2 is linearly dependent. b. If 1 is linearly independent, know not about 2 . c. If 2 is linearly independent, so is 1 . d. If 2 is linearly dependent, know not about 1 . 4. If S is linearly independent and \ then is linearly dependent iff u is a linear combination of elements of S. ? ( ) Proof: Suppose ? = ? ? , ( ?? ) 1 ? = 0 (non-trivial l.c. of distinct elements of is linearly dependent....
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