Solved: Suppose an m × n matrix A has n pivot columns.

Chapter 1, Problem 40E

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QUESTION:

Suppose an \(m \times n\) matrix A has n pivot columns. Explain why for each b in \(\mathbb{R}^{m}\) the equation Ax = b has at most one solution. [Hint: Explain why Ax = b cannot have infinitely many solutions.]

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QUESTION:

Suppose an \(m \times n\) matrix A has n pivot columns. Explain why for each b in \(\mathbb{R}^{m}\) the equation Ax = b has at most one solution. [Hint: Explain why Ax = b cannot have infinitely many solutions.]

ANSWER:

Solution: 

Step 1: Suppose an m × n matrix A has n pivot columns.

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