MATH221 April 2009
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Question 12 (f)
If T: is a linear transformation, and if are vectors in such that are linearly independent, then must be linearly independent.
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The answer is true. Suppose that
where . We want to show that .
Applying T to the above equation, we find
Since we are given that , and are linearly independent, the above equality forces , which is what we wanted to show.
Therefore, are linearly independent.
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