Let A be a 3 × 3 matrix with the property that the linear

Chapter , Problem 22E

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QUESTION:

Let A be a 3 × 3 matrix with the property that the linear transformation x ? Ax maps ?3 onto ?3. Explain why the transformation must be one-to-one.

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QUESTION:

Let A be a 3 × 3 matrix with the property that the linear transformation x ? Ax maps ?3 onto ?3. Explain why the transformation must be one-to-one.

ANSWER:

Problem 22ELet A be a 3 × 3 matrix with the property that the linear transformation x Ax maps 3 onto 3. Explain why the transformation must be one-to-one.Solution:Step 1If A be a 3

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