I'm stuck on how to begin this problem...

Let (c1, c2) be a solution to the 2x2 system

A11X1 + A12X2 = 0

A21X1 + A22X2 = 0

Show that for any real number alpha (a) the ordered pair (ac1, ac2) is also a solution.

Printable View

- March 30th 2008, 03:59 PMpakmanShowing a solution for system of equations
I'm stuck on how to begin this problem...

Let (c1, c2) be a solution to the 2x2 system

A11X1 + A12X2 = 0

A21X1 + A22X2 = 0

Show that for any real number alpha (a) the ordered pair (ac1, ac2) is also a solution. - March 30th 2008, 05:03 PMteuthid
Plug in ...

Therefore, if , then is also a solution to .

then repeat the process of the second equation. This process can be done more quickly if you use matrix notation:

is a solution to

so, if we test ...

therefore is also a solution to