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## Homework Statement

Show that if A = {v_1, v_2, v_3. . .v_n} is a linearly independent set then any subset of A is also linearly independent

## Homework Equations

proof.

## The Attempt at a Solution

so if A is a set of vectors

[v_1 ]

[v_2 ]

[v_3 ]

[. . . ]

[v_n ]

for it to be independent then the determinant must NOT be zero and so far I know that det are just for square matrices.

therefore A must be a square matrix with a det not = to zero.

therefore it must be possible to reduce it to the identity matrix

therefore since the Identity matrix has a leading 1 on different columns/rows you can NOT write any of them as a linear combination of any other ones, therefore any subset would be independent also ??

Im not sure about this since its mostly text and I dont know if I should have more math

. . .

the back of the book just says Proof.

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