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m × n matrix with the property that for all b in m the
Chapter 1, Problem 39E(choose chapter or problem)
Suppose A is an \(m \times n\) matrix with the property that for all b in \(\mathbb{R}^{m}\) the equation Ax = b has at most one solution. Use the definition of linear independence to explain why the columns of A must be linearly independent.
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QUESTION:
Suppose A is an \(m \times n\) matrix with the property that for all b in \(\mathbb{R}^{m}\) the equation Ax = b has at most one solution. Use the definition of linear independence to explain why the columns of A must be linearly independent.
ANSWER:Solution: Step 1: Suppose A is an m × n matrix with the property that for all b in m the equation Ax = b has at most one solution.Step2: To explain why the columns of A must be linearly independent.Step3: Let's Ax=b has at most one solution for all b,