1. Let T + T([y]) = [2x+3y]. (a) Is v= 3] 2 in the kernel of...

   

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1. Let T + T([y]) = [2x+3y]. (a) Is v= 3] 2 in the kernel of T? Explain. (b) Find a vector in R2 that is not in the range of T. 2. Define the linear transformation T: R-R by 1-1-1 1 T(v) = 2 0-1 -3 -1 1 5 1-2 4 -7 11 (a) State the dimension of the domain and codomain of T. (b) Find a basis for the kernel of T. State the nullity of T. (c) Find a basis for the range of T. State the rank of T (d) Is T one-to-one? Explain. (e) Is T onto? Explain. (f) Is T invertible? Explain. 1. Let T + T([y]) = [2x+3y]. (a) Is v= 3] 2 in the kernel of T? Explain. (b) Find a vector in R2 that is not in the range of T. 2. Define the linear transformation T: R-R by 1-1-1 1 T(v) = 2 0-1 -3 -1 1 5 1-2 4 -7 11 (a) State the dimension of the domain and codomain of T. (b) Find a basis for the kernel of T. State the nullity of T. (c) Find a basis for the range of T. State the rank of T (d) Is T one-to-one? Explain. (e) Is T onto? Explain. (f) Is T invertible? Explain.