Known vector group I: A1, A2, A3; II: A1, A2, A3, A4; III:a1 If the rank of each vector group is R (I) = R (II) = 3, R (III) = 4, it is proved that vector group IV: A1, A2, A3, a5-a4 are linearly independent

Because R (A1, A2, A3) = 3, so A1, A2, A3 are linearly independent, and because R (A1, A2, A3, A4) = 3, so A1, A2, A3, A4 are related, so A4 can be expressed linearly by A1, A2, A3. Because R (A1, A2, A3, A5) = 4, so A1, A2, A3, A5 are linearly independent, so A5 cannot be expressed linearly by A1, A2, A3, so A5

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