Question: 1. A function T from R to RM is given. Either prove that T is a linear transformation by showing that it satisfies the two

1. A function T from R" to RM is given. Either prove that T is a linear transformation by showing that it satisfies the two requirements of linear transformation, or show that it is not by using a counterexample with numbers. T(X1, X2, X3) = -7x1 + 2x2 - X3 + 4 2. A function T from R" to Rm is given. Either prove that T is a linear transformation by showing that it satisfies the two requirements of linear transformation, or show that it is not by using a counterexample with numbers. T(X1, X2) = (0, X1, X2) 3. A function T that maps polynomials from P2 to the real number line R is given. Either prove that T is a linear transformation by showing that it satisfies the two requirements of a linear transformation, or show that it is not by using a counterexample with numbers. T(do + aix + azx2) = do Note: all the coefficients are arbitrary constants

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