Math Problem Statement
Suppose 𝑏, 𝑐 ∈ 𝐑. Define 𝑇∶ 𝐑 3 → 𝐑2 by 𝑇(𝑥, 𝑦, 𝑧) = (2𝑥 − 4𝑦 + 3𝑧 + 𝑏, 6𝑥 + 𝑐𝑥𝑦𝑧). Show that 𝑇 is linear if and only if 𝑏 = 𝑐 = 0
Solution
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Math Problem Analysis
Mathematical Concepts
Linear transformations
Additivity
Homogeneity
Formulas
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Theorems
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Suitable Grade Level
Advanced undergraduate
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