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eimsori [14]
3 years ago
6

39. Suppose A is an m n matrix with the property that for all b in Rm the equation Ax D b has at most one solution. Use the defi

nition of linear independence to explain why the columns of A must be linearly independent.
Mathematics
1 answer:
Anna [14]3 years ago
5 0

Answer: trivial solution is the only solution to Ax = 0, therefore columns must be linearly independent.

Step-by-step explanation: Recall that the columns of A are linearly independent if and only Ax = 0 had only the trivial solution. Since Ax = b has at most one solution, therefore the only solution to Ax = 0 is the trivial solution and the column vectors must be linearly independent.

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