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Suppose {v1, v2} is a linearly independent set in n. Show
Chapter , Problem 18E(choose chapter or problem)
QUESTION:
Suppose {v1, v2} is a linearly independent set in ?n. Show that {v1, v1 + v2} is also linearly independent.
Questions & Answers
QUESTION:
Suppose {v1, v2} is a linearly independent set in ?n. Show that {v1, v1 + v2} is also linearly independent.
ANSWER:SolutionStep 1 of 2Let {v1 , v2 , v1+v2 } is a linearly independent set in n. So, the vector equation will be x1 v1 + x2 v2 + x3 (v1 + v2 ) = 0 x1 v1 + x2 v2 + x3 v1 + x3v2 = 0 (x1 + x3 )v1 + (x2 + x3 ) v2 = 0