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In: Advanced Math

Let A be an m x n matrix. Prove that Ax = b has at least...

  1. Let A be an m x n matrix. Prove that Ax = b has at least one solution for any b if and only if A has linearly independent rows.

  2. Let V be a vector space with dimension 3, and let V = span(u, v, w). Prove that u, v, w are linearly independent (in other words, you are being asked to show that u, v, w form a basis for V)

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