ach team must have an odd number of Masters, and any two teams must have an even number of Masters in common....
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The Jedi Council is forming assault teams. Each team must have an odd number of Masters, and any two teams must have an even number of Masters in common. Show that the number of different teams cannot be larger than the size of the Council.
The problem can be solved using Linear Algebra. A hint was given to encode the teams as elements of $mathbb{F}^n$ where $mathbb{F} = mathbb{Z}_2$. Show that the teams are independent using the dot product and argue using dimension. Any ideas?
linear-algebra
asked Dec 6 '18 at 19:17
johnny133253johnny133253
302110
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add a comment |
$begingroup$
The Jedi Council is forming assault teams. Each team must have an odd number of Masters, and any two teams must have an even number of Masters in common. Show that the number of different teams cannot be larger than the size of the Council.
The problem can be solved using Linear Algebra. A hint was given to encode the teams as elements of $mathbb{F}^n$ where $mathbb{F} = mathbb{Z}_2$. Show that the teams are independent using the dot product and argue using dimension. Any ideas?
linear-algebra
asked Dec 6 '18 at 19:17
johnny133253johnny133253
302110
$endgroup$
1
$begingroup$
Have you tried to apply the hint? Where are you having difficulty?
$endgroup$
– saulspatz
Dec 6 '18 at 19:21
$begingroup$
I am not sure how to encode the teams as elements of $mathbb{F}^n$. I have thought about it but I have not made any progress.
$endgroup$
– johnny133253
Dec 6 '18 at 19:38
1
$begingroup$
Number the masters from $1$ to $n$. Then encode a team as a vector where component $k$ is $1$ if and only if master $k$ is on the team.
$endgroup$
– saulspatz
Dec 6 '18 at 19:39
$begingroup$
Makes sense. I will try that. Thank you.
$endgroup$
– johnny133253
Dec 6 '18 at 19:42
add a comment |
$begingroup$
The Jedi Council is forming assault teams. Each team must have an odd number of Masters, and any two teams must have an even number of Masters in common. Show that the number of different teams cannot be larger than the size of the Council.
The problem can be solved using Linear Algebra. A hint was given to encode the teams as elements of $mathbb{F}^n$ where $mathbb{F} = mathbb{Z}_2$. Show that the teams are independent using the dot product and argue using dimension. Any ideas?
linear-algebra
asked Dec 6 '18 at 19:17
johnny133253johnny133253
302110
$endgroup$
The Jedi Council is forming assault teams. Each team must have an odd number of Masters, and any two teams must have an even number of Masters in common. Show that the number of different teams cannot be larger than the size of the Council.
The problem can be solved using Linear Algebra. A hint was given to encode the teams as elements of $mathbb{F}^n$ where $mathbb{F} = mathbb{Z}_2$. Show that the teams are independent using the dot product and argue using dimension. Any ideas?
linear-algebra
linear-algebra
asked Dec 6 '18 at 19:17
johnny133253johnny133253
302110
asked Dec 6 '18 at 19:17
johnny133253johnny133253
302110
asked Dec 6 '18 at 19:17
johnny133253johnny133253
302110
asked Dec 6 '18 at 19:17
johnny133253johnny133253
302110
asked Dec 6 '18 at 19:17
johnny133253johnny133253
302110
302110
1
$begingroup$
Have you tried to apply the hint? Where are you having difficulty?
$endgroup$
– saulspatz
Dec 6 '18 at 19:21
$begingroup$
I am not sure how to encode the teams as elements of $mathbb{F}^n$. I have thought about it but I have not made any progress.
$endgroup$
– johnny133253
Dec 6 '18 at 19:38
1
$begingroup$
Number the masters from $1$ to $n$. Then encode a team as a vector where component $k$ is $1$ if and only if master $k$ is on the team.
$endgroup$
– saulspatz
Dec 6 '18 at 19:39
$begingroup$
Makes sense. I will try that. Thank you.
$endgroup$
– johnny133253
Dec 6 '18 at 19:42
add a comment |
1
$begingroup$
Have you tried to apply the hint? Where are you having difficulty?
$endgroup$
– saulspatz
Dec 6 '18 at 19:21
$begingroup$
I am not sure how to encode the teams as elements of $mathbb{F}^n$. I have thought about it but I have not made any progress.
$endgroup$
– johnny133253
Dec 6 '18 at 19:38
1
$begingroup$
Number the masters from $1$ to $n$. Then encode a team as a vector where component $k$ is $1$ if and only if master $k$ is on the team.
$endgroup$
– saulspatz
Dec 6 '18 at 19:39
$begingroup$
Makes sense. I will try that. Thank you.
$endgroup$
– johnny133253
Dec 6 '18 at 19:42
1
1
$begingroup$
Have you tried to apply the hint? Where are you having difficulty?
$endgroup$
– saulspatz
Dec 6 '18 at 19:21
$begingroup$
Have you tried to apply the hint? Where are you having difficulty?
$endgroup$
– saulspatz
Dec 6 '18 at 19:21
$begingroup$
I am not sure how to encode the teams as elements of $mathbb{F}^n$. I have thought about it but I have not made any progress.
$endgroup$
– johnny133253
Dec 6 '18 at 19:38
$begingroup$
I am not sure how to encode the teams as elements of $mathbb{F}^n$. I have thought about it but I have not made any progress.
$endgroup$
– johnny133253
Dec 6 '18 at 19:38
1
1
$begingroup$
Number the masters from $1$ to $n$. Then encode a team as a vector where component $k$ is $1$ if and only if master $k$ is on the team.
$endgroup$
– saulspatz
Dec 6 '18 at 19:39
$begingroup$
Number the masters from $1$ to $n$. Then encode a team as a vector where component $k$ is $1$ if and only if master $k$ is on the team.
$endgroup$
– saulspatz
Dec 6 '18 at 19:39
$begingroup$
Makes sense. I will try that. Thank you.
$endgroup$
– johnny133253
Dec 6 '18 at 19:42
$begingroup$
Makes sense. I will try that. Thank you.
$endgroup$
– johnny133253
Dec 6 '18 at 19:42
add a comment |
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1
$begingroup$
Have you tried to apply the hint? Where are you having difficulty?
$endgroup$
– saulspatz
Dec 6 '18 at 19:21
$begingroup$
I am not sure how to encode the teams as elements of $mathbb{F}^n$. I have thought about it but I have not made any progress.
$endgroup$
– johnny133253
Dec 6 '18 at 19:38
1
$begingroup$
Number the masters from $1$ to $n$. Then encode a team as a vector where component $k$ is $1$ if and only if master $k$ is on the team.
$endgroup$
– saulspatz
Dec 6 '18 at 19:39
$begingroup$
Makes sense. I will try that. Thank you.
$endgroup$
– johnny133253
Dec 6 '18 at 19:42