hello,

i have 6 variables

a=5

b=10

c=7

d=9

x=1

y=2

when i solve this equation using gauss-jordan it gives me wrong answer

a⊕0⊕c⊕0⊕0⊕0=2

0⊕b⊕0⊕d⊕0⊕0=3

a⊕0⊕0⊕0⊕x⊕0=4

0⊕b⊕0⊕0⊕0⊕y=8

0⊕0⊕c⊕0⊕x⊕0=6

0⊕0⊕0⊕d⊕0⊕y=11

⊕ is XOR

thanks for your help :)

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- Jul 18th 2012, 10:51 PMMathGeek1983solve an xor'd linear equation
hello,

i have 6 variables

a=5

b=10

c=7

d=9

x=1

y=2

when i solve this equation using gauss-jordan it gives me wrong answer

a⊕0⊕c⊕0⊕0⊕0=2

0⊕b⊕0⊕d⊕0⊕0=3

a⊕0⊕0⊕0⊕x⊕0=4

0⊕b⊕0⊕0⊕0⊕y=8

0⊕0⊕c⊕0⊕x⊕0=6

0⊕0⊕0⊕d⊕0⊕y=11

⊕ is XOR

thanks for your help :) - Jul 19th 2012, 06:14 AMemakarovRe: solve an xor'd linear equation
The initial augmented matrix is

Code:`1 0 1 0 0 0 = 2`

0 1 0 1 0 0 = 3

1 0 0 0 1 0 = 4

0 1 0 0 0 1 = 8

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

Code:`1 0 1 0 0 0 = 2`

0 1 0 1 0 0 = 3

0 0 1 0 1 0 = 6

0 1 0 0 0 1 = 8

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

Code:`1 0 1 0 0 0 = 2`

0 1 0 1 0 0 = 3

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

Code:`1 0 1 0 0 0 = 2`

0 1 0 1 0 0 = 3

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

0 0 0 0 0 0 = 0

0 0 0 1 0 1 = 11

Code:`1 0 1 0 0 0 = 2`

0 1 0 1 0 0 = 3

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

0 0 0 0 0 0 = 0

0 0 0 0 0 0 = 0

Code:`1 0 1 0 0 0 = 2`

0 1 0 1 0 0 = 3

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

Code:`1 0 1 0 0 0 = 2`

0 1 0 0 0 1 = 8

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

Code:`1 0 0 0 1 0 = 4`

0 1 0 0 0 1 = 8

0 0 1 0 1 0 = 6

0 0 0 1 0 1 = 11

d + 2 = 11; d = 9

c + 1 = 6; c = 7

b + 2 = 8; b = 10

a + 1 = 4; a = 5 - Jul 19th 2012, 06:26 AMMathGeek1983Re: solve an xor'd linear equation
Thanks for the reply, emakarov

but what if x and y werent given ?? what will i do ? - Jul 19th 2012, 06:44 AMemakarovRe: solve an xor'd linear equation
This is an underdetermined system, so it has infinitely many solutions. For each value of x and y, there is a unique solution for a, b, c and d. For example, for x = 2 and y = 1 we have a = 6, b = 9, c = 4 and d = 10.

- Jul 19th 2012, 10:18 AMMathGeek1983Re: solve an xor'd linear equation
Thank you so much emakarov! you are a life saver! :)