Does there exist a linear transformation T : R2 → R4 such that Range(T ) ={(x1, x2, x3, x4) : x1 + x2 + x3 + x4 = 0
Question
Solution 1
Yes, there does exist a linear transformation T : R2 → R4 such that Range(T) = {(x1, x2, x3, x4) : x1 + x2 + x3 + x4 = 0}.
Here's a step-by-step explanation:
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Define the linear transformation T : R2 → R4 as T(x, y) = (x, y, -x, -y).
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For any (x, y) in R2, T(x, y) is in the set {(x1, x2, x3, Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
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