(1.2.5)--英3.2.2 Correlation of Vector Gro线性代数线性代数

LinearAlgebra3.2.2PropertiesofLinearCorrelationofVectorGroupsTheorem1VectorgroupA:islinearlydependentThereisatleastoneofthevectorsisalinearcombinationofother−1vectors.𝑚Proof(Sufficiency)Givenavectorin(suchas)thatcanbelinearlyrepresentedbytheremainingvectors,so𝛼𝑚=𝜆1𝛼1+𝜆2𝛼2+⋯+𝜆𝑚−1𝛼𝑚−1⇒𝜆1𝛼1+𝜆2𝛼2+⋯+𝜆𝑚−1𝛼𝑚−1+(−1)𝛼𝑚=𝑂Obviouslyarenotallzero,soislinearlydependent.Thatis...