1. Consider the following maps of Euclidean vectors P: R R and Q : R...

 

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1. Consider the following maps of Euclidean vectors P: R³ → R³ and Q : R³ R³ defined by (E]) - [ ([:]) P 3x - 2y-2z 2x - y - 2z andQ -x-y + 5z Without writing a proof, explain why only one of these maps is likely to be a linear transformation. 2. Consider the following map of Euclidean vectors S: R² → R² s([:])=[²] -7x² S Prove that T is a linear transformation. - Prove that S is not a linear transformation. 3. Consider the following map of Euclidean vectors T: R² R² = T " ( [*]) - [6 + 10% ]. 6x+10y - 4x - 6y -4y² - 8xz x-5y - 8z y+z 1. Consider the following maps of Euclidean vectors P: R³ → R³ and Q : R³ R³ defined by (E]) - [ ([:]) P 3x - 2y-2z 2x - y - 2z andQ -x-y + 5z Without writing a proof, explain why only one of these maps is likely to be a linear transformation. 2. Consider the following map of Euclidean vectors S: R² → R² s([:])=[²] -7x² S Prove that T is a linear transformation. - Prove that S is not a linear transformation. 3. Consider the following map of Euclidean vectors T: R² R² = T " ( [*]) - [6 + 10% ]. 6x+10y - 4x - 6y -4y² - 8xz x-5y - 8z y+z

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Question 1 The map Q is likely to be a linear transformation because it only multi... View the full answer