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On whether n + 1 n-dimensional vectors are linearly related For example, is a = (1,1,1) B = (1,2,3) C = (4,5,6) d = (7,8,9) ABCD necessarily related?
It's
It can be proved to the contrary
N + 1 n-dimensional vector must be linear correlation, can you roughly explain it, help to understand and remember!
Conclusion: 1. If the number of rows of a in AX = 0 is less than the number of columns, that is, the number of equations is less than the number of unknowns, then the equations have non-zero solutions. 2. Vector group A1,..., as linear correlation homogeneous linear equations (A1,..., as) x = 0 have non-zero solutions
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