Question

Let u=[3 0] and v=[1 2]. Compute the area of the parallelogram determined by u,v, u+v, and 0, and compute the determinant of [u v]. How do they compare? Replace the first entry of v by an arbitrary number x, and repeat the problem. Draw a picture and explain what you find.

Answer 1

@Loser66

Answer 2

@Loser66

Answer 3

draw it out,

Answer 4

draw the vectors

Answer 5

Okay I was about to draw that...

Answer 6

and the area of that parallelogram is computed by u dot v

Answer 7

kk

Answer 8

to get det [u v] just put them there to calculate
you will have det = 6 and area =3 so, area = 1/2 det

Answer 9

so dotting them gives us the area huh? what was the point of det(u v)