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compute sum of the components of the solution to a linear equation
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Given $A x = b$, where $Ain mathbb R^ntimes n$ is invertible. Let $x=(x_1, cdots, x_n)^T$. How to compute $sum_i=1^n x_i$ without solving the equation? For a given $Cin mathbb R$, how to check if $x_1+cdots +x_n = C$ is consistent with $Ax=b$ without solving the equation?
linear-algebra
asked Jul 19 at 18:57
user32828
1409
add a comment |Â
up vote
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down vote
favorite
Given $A x = b$, where $Ain mathbb R^ntimes n$ is invertible. Let $x=(x_1, cdots, x_n)^T$. How to compute $sum_i=1^n x_i$ without solving the equation? For a given $Cin mathbb R$, how to check if $x_1+cdots +x_n = C$ is consistent with $Ax=b$ without solving the equation?
linear-algebra
asked Jul 19 at 18:57
user32828
1409
I guess you are not allowed to compute the inverse of $A$?
– lanskey
Jul 19 at 21:43
No. Don't want to compute the inverse of $A$.
– user32828
Jul 19 at 21:58
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given $A x = b$, where $Ain mathbb R^ntimes n$ is invertible. Let $x=(x_1, cdots, x_n)^T$. How to compute $sum_i=1^n x_i$ without solving the equation? For a given $Cin mathbb R$, how to check if $x_1+cdots +x_n = C$ is consistent with $Ax=b$ without solving the equation?
linear-algebra
asked Jul 19 at 18:57
user32828
1409
Given $A x = b$, where $Ain mathbb R^ntimes n$ is invertible. Let $x=(x_1, cdots, x_n)^T$. How to compute $sum_i=1^n x_i$ without solving the equation? For a given $Cin mathbb R$, how to check if $x_1+cdots +x_n = C$ is consistent with $Ax=b$ without solving the equation?
linear-algebra
asked Jul 19 at 18:57
user32828
1409
asked Jul 19 at 18:57
user32828
1409
asked Jul 19 at 18:57
user32828
1409
asked Jul 19 at 18:57
user32828
1409
1409
I guess you are not allowed to compute the inverse of $A$?
– lanskey
Jul 19 at 21:43
No. Don't want to compute the inverse of $A$.
– user32828
Jul 19 at 21:58
add a comment |Â
I guess you are not allowed to compute the inverse of $A$?
– lanskey
Jul 19 at 21:43
No. Don't want to compute the inverse of $A$.
– user32828
Jul 19 at 21:58
I guess you are not allowed to compute the inverse of $A$?
– lanskey
Jul 19 at 21:43
I guess you are not allowed to compute the inverse of $A$?
– lanskey
Jul 19 at 21:43
No. Don't want to compute the inverse of $A$.
– user32828
Jul 19 at 21:58
No. Don't want to compute the inverse of $A$.
– user32828
Jul 19 at 21:58
add a comment |Â
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I guess you are not allowed to compute the inverse of $A$?
– lanskey
Jul 19 at 21:43
No. Don't want to compute the inverse of $A$.
– user32828
Jul 19 at 21:58