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Changing Variables in Subsets of ℝ2 and ℝ3 -HW Problems
Determine if the maps from ℝ2 to ℝ2 are one-to-one and/or onto.
1. 𝑆(𝑥, 𝑦) = (2𝑥, 2𝑦)
2. 𝑆(𝑥, 𝑦) = (𝑒 𝑥 , 𝑦 3 )
3. 𝑇(𝑥, 𝑦) = (𝑥 3 , 𝑦 3 )
Determine if the maps from ℝ3 to ℝ3 are one-to-one and/or onto.
4. 𝑇(𝑥, 𝑦, 𝑧) = (2𝑥, 4𝑦, 6𝑧)
5. 𝑆(𝑥, 𝑦, 𝑧) = (2𝑥, 4𝑦, 𝑥)
6. 𝑆(𝑥, 𝑦, 𝑧) = (𝑒 𝑧 , 𝑒 𝑥 , 𝑒 𝑦 )
Changing Variables in Subsets of ℝ2 and ℝ3 -HW Problems
Determine if the maps from ℝ2 to ℝ2 are one-to-one and/or onto.
1. 𝑆(𝑥, 𝑦) = (2𝑥, 2𝑦)
2. 𝑆(𝑥, 𝑦) = (𝑒 𝑥 , 𝑦 3 )
3. 𝑇(𝑥, 𝑦) = (𝑥 3 , 𝑦 3 )
Determine if the maps from ℝ3 to ℝ3 are one-to-one and/or onto.
4. 𝑇(𝑥, 𝑦, 𝑧) = (2𝑥, 4𝑦, 6𝑧)
5. 𝑆(𝑥, 𝑦, 𝑧) = (2𝑥, 4𝑦, 𝑥)
6. 𝑆(𝑥, 𝑦, 𝑧) = (𝑒 𝑧 , 𝑒 𝑥 , 𝑒 𝑦 )
