- #1
_Bd_
- 109
- 0
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 don't know if I should have more math
. . .
the back of the book just says Proof.
Last edited: