Question

For these matrices:
S=[u,v,-v,u] T=[x,y,-y,x]
NOTE: these matrices are 2x2 matrices, the first two on the top row and the last two on the bottom row. (sorry I can't express them properly here).
a) Find the determinants of S, T and ST
b) Use ordinary algebra to verify that det(S)det(T)=det(ST)
c) Express (7^2 + 2^2)(4^2 + 1^2) as a sum of squares of two integers.

Answer 1

for any 2X2 matrix
a b
c d
det = ad - bc

Answer 2

give me just a sec k?

Answer 3

i will scan what i have so far... it isn't complete

Answer 4

thanks everyone - especially myininaya :)

Answer 5

i was fixing to type this i think i will just scan it lol

Answer 6

good idea, much easier :)

Answer 7

you know a^2+2ab+b^2=(a+b)^2
and
a^2-2ab+b^2=(a-b)^2
right?

Answer 8

yes

Answer 9

do you see i add in a zero so I could write (ux-vy)^2+(vx+yu)^2

Answer 10

yes indeed :) thank you so much!!!

Answer 11

k cool are there any questions?
please let me know if you don't understand something

Answer 12

i think i understand it all :) thanks :)