3 23 points Matrices as Lincar Transformations Determinants

3 (23 points) Matrices as Lincar Transformations & Determinants 2. 3, 2, 7, 9 Let and (a) Compute the vectors ui = Ae, and u2 = Ae2. (b) Sketch e and e and the square they determine in the ay-plane with both axes from -5 to 5. Sketch u and u2 and the parallelogram they determine on a second set of axes with with both axes from -5 to 5. We can think of the matrix A as representing a map, or function, that takes vectors in R2 to vectors in R2. This type of map is called

Solution

a.)
u1=Ae1
So, u1 = [2]
[1]

u2 = [1]
[3]

c.) Determinant of A = 2*3 - 1*1

Determinant = 6-1

Determinant = 5