1. The problem statement, all variables and given/known data for the following, find (a) the image of the indicated set under the given linear transformation and (b) the area or volume of the image question 1: P is the paralellogram in R^2 with corner (0,0) spanned by (1,-1) and (4,7); It undergoes the transformation T(x) = (3x + 4y, 4x + 5y) question 2: P is the parallelepiped with corner (1,1,1) spanned by (1,1,2), (1,2,1), and (2,1,1). T(x) = (3y, -4x, 5z) 2. Relevant equations I know the area of a parallelogram = ||a x b|| (cross product between vectors a and b) The volume of a parallelepipid = ||a x b|| . c (cross product of vectors a & b. Then the dot product is used between that answer and vector c to obtain volume) The area of a transformed parallelogram = |det(transformation matrix)|*(area of parallelogram) The volume of a transformed parallelepiped = |det(transformation matrix)|*(volume of parallelepipid) 3. The attempt at a solution for question 1, I have the transformation points as (0,0) (-1,-1) and (-16,-19). For the area, I took the cross product of vectors a and b (vector a = (-1,-1) vector b = (-16,-19)) and got 3. I got the determinant equals 1. So i got the area to be 3, but the answer key says it is 11. For question 2, I'm just completely confused to be quite honest.