
Matrix help
Hi guys. Strange question here but i dont know how to solve and its for revision.
let A = 2x2 matrix ( 2 is the top left entry, 1 the top right entry, 7 the bottom left and 4 the bottom right)
B = 2x2 matrix (3 the top left entry, x the top right, y the bottom left and 4 the bottom right)
determine all the possible values for x and y, but such that AB = BA
please help :( this is a revision question for an upcoming exam so i really need to know how to do it. thanks!

Re: Matrix help
According to the question,
Therefore you have the following equations,

Re: Matrix help
But how do i get x and y from there?
I tried one way but i dont know how to find the inverse of a four square (and im not meant to in my course)

Re: Matrix help
Quote:
Originally Posted by
sbhatnagar

Re: Matrix help
you're not meant to find the inverse of anything.
from 6 + y = 6 + 7x, we have:
y = 7x. so if we find out x, we will know y.
from 2x + 4 = 3 + 4x we get:
2x  1 = 0, so x = 1/2.
we need to check the last two equations for consistency:
21 + 4(7/2) = 21 + 14 = 35
2(7/2) + 28 = 7 + 28 = 35, the 3rd equation is consistent with the first 2.
7(1/2) + 16 = 7/2 + 32/2 = 39/2
7/2 + 16 = 7/2 + 32/2 = 39/9, all 4 equations are consistent.
therefore B can only be:
[3 1/2]
[7/2 4]
(no inverses were harmed in the making of this film)