Linear Algebra System Solution: (x,y,z) = (a,b,a), Non-Integer a + b Calculation

[jcharky]

The solution of the system

ax + ay - z = 1
x - ay - az = -1
ax - y + az = 1

is (x,y,z) = (a,b,a). If a is not an integer, what is the numberical value of a + b.

So I guess i should plug in (a,b,a) for (x,y,z) first..

a^2 + ab - a = 1
a - ab + a^2 = -1
a^2 - b - a^2 = 1

I am not sure how to solve for a + b though and I am not sure how part that a is not an integer comes into play can someone help?

 

[dachikid]

Paul's Online Math Notes is a website full of great examples and explanations on various mathematical disciplines. The answers you seek are at the following url:

http://tutorial.math.lamar.edu/Classes/LinAlg/LinAlg.aspx

 

[tiny-tim]

Welcome to PF!

Hi jcharky ! Welcome to PF!

(try using the X² tag just above the Reply box )

Your second and third equations have a² the wrong way round.