A linear programming question, no feasible solution question
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I'm studying for a test and I came across this question:
Let $a_1, a_2, . . . a_m in Bbb R^n$
such that $m > n+1$. Assume that for the set of m inequalities $a_i^t x ≤ b_i$
there is no feasible solution. Prove that there are $n + 1$ inequalities out of the $m$ which are not feasible.
Any advice?
Thanks
linear-algebra
asked Nov 18 at 13:46
John Doe
62
add a comment |
up vote
0
down vote
favorite
I'm studying for a test and I came across this question:
Let $a_1, a_2, . . . a_m in Bbb R^n$
such that $m > n+1$. Assume that for the set of m inequalities $a_i^t x ≤ b_i$
there is no feasible solution. Prove that there are $n + 1$ inequalities out of the $m$ which are not feasible.
Any advice?
Thanks
linear-algebra
asked Nov 18 at 13:46
John Doe
62
$m>n+1$ or $m geq n+1$ ?
– Jean Marie
Nov 18 at 17:42
m $> n+1$ I'm also confused about why the strict inequality is required
– John Doe
Nov 19 at 13:03
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I'm studying for a test and I came across this question:
Let $a_1, a_2, . . . a_m in Bbb R^n$
such that $m > n+1$. Assume that for the set of m inequalities $a_i^t x ≤ b_i$
there is no feasible solution. Prove that there are $n + 1$ inequalities out of the $m$ which are not feasible.
Any advice?
Thanks
linear-algebra
asked Nov 18 at 13:46
John Doe
62
I'm studying for a test and I came across this question:
Let $a_1, a_2, . . . a_m in Bbb R^n$
such that $m > n+1$. Assume that for the set of m inequalities $a_i^t x ≤ b_i$
there is no feasible solution. Prove that there are $n + 1$ inequalities out of the $m$ which are not feasible.
Any advice?
Thanks
linear-algebra
linear-algebra
asked Nov 18 at 13:46
John Doe
62
asked Nov 18 at 13:46
John Doe
62
edited Nov 18 at 14:01
asked Nov 18 at 13:46
John Doe
62
asked Nov 18 at 13:46
John Doe
62
asked Nov 18 at 13:46
John Doe
62
62
$m>n+1$ or $m geq n+1$ ?
– Jean Marie
Nov 18 at 17:42
m $> n+1$ I'm also confused about why the strict inequality is required
– John Doe
Nov 19 at 13:03
add a comment |
$m>n+1$ or $m geq n+1$ ?
– Jean Marie
Nov 18 at 17:42
m $> n+1$ I'm also confused about why the strict inequality is required
– John Doe
Nov 19 at 13:03
$m>n+1$ or $m geq n+1$ ?
– Jean Marie
Nov 18 at 17:42
$m>n+1$ or $m geq n+1$ ?
– Jean Marie
Nov 18 at 17:42
m $> n+1$ I'm also confused about why the strict inequality is required
– John Doe
Nov 19 at 13:03
m $> n+1$ I'm also confused about why the strict inequality is required
– John Doe
Nov 19 at 13:03
add a comment |
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$m>n+1$ or $m geq n+1$ ?
– Jean Marie
Nov 18 at 17:42
m $> n+1$ I'm also confused about why the strict inequality is required
– John Doe
Nov 19 at 13:03