Show all your work. be sure to write your work and answers clearly and neatly. use your oun paper. 1. define t : t(p("(z) +27(z) + p(z). also, let u = z? +3x + 1 and a) find t(u) and t(v). b) is t(u + v)- t(u) + t(v)? 2. determine if w =- is in the null space of t(x)-ax, where 2 641 l-5 -4 1 3. define t: r3 r2 by find all the vectors that are mapped to 0. 4. let a be the matrix 3 -6 9 0 a- 2 4 7 2 3 -6 6 6, determine a basis for the null space of t(x)-ax. 5. let a be the matrix a-1 5 -4 0 2-2 6 find a basis for the range of t(x) = ax. 6. consider the linear transformation t( a) determine if the set [t(ei), t(e2)) is a basis for r2 b) is this linear transformation one-to-one? explain.