MATH 251 Lecture 1: 16.3

15. Use the transformation z = u/v, y = uu to evaluate the integral sum (2 y) dz dy. 2 Jy/4

Please show all your work. Be sure to urite your work and answers clearly and neatly Use your oun paper 1. Define T :???be T(p(z)) = p"(z) + 2p'(z) + plz). Also, let u " z2 + 3z + 1 and v=z+1. a) Find T(u) and T(v). b) Is T(u + v) = T(u) + T(v)? 2, Determine if w =-1 | is in the null space of T(x)-Ax, where A--3 2 5 3. Define T:R3R2 by Find all the vectors that are mapped to 0. 4. Let A be the matrix 3 -6 9 0 A 2 -4 72 3 -6 6 6 Determine a basis for the null space of T(x) 5. Let A be the matrix Ax. 15 2 1015 A=115-402-26 Find a basis for the range of T(x)-Ax 6. Consider the linear transformation T ( ) ? 5y a) Determine if the set (T(ei),T(e2)) is a basis for R2 b) Is this linear transformation one-to-one? Explain.

Please show all your work. Be sure to urite your work and answers clearly and neatly Use your oun paper 1. Define T :???be T(p(z)) = p"(z) + 2p'(z) + plz). Also, let u " z2 + 3z + 1 and v=z+1. a) Find T(u) and T(v). b) Is T(u + v) = T(u) + T(v)? 2, Determine if w =-1 | is in the null space of T(x)-Ax, where A--3 2 5 3. Define T:R3R2 by Find all the vectors that are mapped to 0. 4. Let A be the matrix 3 -6 9 0 A 2 -4 72 3 -6 6 6 Determine a basis for the null space of T(x) 5. Let A be the matrix Ax. 15 2 1015 A=115-402-26 Find a basis for the range of T(x)-Ax 6. Consider the linear transformation T ( ) ? 5y a) Determine if the set (T(ei),T(e2)) is a basis for R2 b) Is this linear transformation one-to-one? Explain.