1) Show that the function T((a,b)) = (2a-b,6a+b) is a linear transformation from R to R....

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1) Show that the function T((a,b)) = (2a-b,6a+b) is a linear transformation from R² to R². 2) Show that the function T:R³ R³ given by T((a,b,c)) = (1+b, a-b, a+b+2c) is not a linear transformation by providing an example of where one of the rules break down. 3) Write the matrix representation for the linear transformation T((a,b)) = (2a-b,a+b,3a-5b). (Yes, you get to assume it is a linear transformation.) 1) Show that the function T((a,b)) = (2a-b,6a+b) is a linear transformation from R² to R². 2) Show that the function T:R³ R³ given by T((a,b,c)) = (1+b, a-b, a+b+2c) is not a linear transformation by providing an example of where one of the rules break down. 3) Write the matrix representation for the linear transformation T((a,b)) = (2a-b,a+b,3a-5b). (Yes, you get to assume it is a linear transformation.)

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