Results 1 to 5 of 5

Math Help - Linear Combination

  1. #1
    Newbie
    Joined
    Feb 2007
    Posts
    18

    Linear Combination

    I have tried to solve this problem:

    714x + 7007y = 7

    but I have not come to a solution yet.

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by jmc1979 View Post
    I have tried to solve this problem:

    714x + 7007y = 7
    Let us find the greatest common divisor by the algorithm mentioned in the Elements.

    7007=(9)714+581
    714=(1)581+133
    581=(4)133+49
    133=(2)49+35
    49=(1)35+14
    35=(2)14+7
    14=(2)7+0

    Work backwards.

    7=35-2*14
    7=35-2(49-35)=3*35-2*49
    7=3(133-2*49)-2*49
    7=3*133-8*49
    7=3*133-8(581-4*133)=35*133-8*581
    7=35(714-581)-8*581=35*714-43*581
    7=35*714-43(7007-9*714)=422*714-43*7007

    Thus,
    714x+7007y=7
    Say for example,
    x=422 and y=-43
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2007
    Posts
    18

    Thank you!

    Thank you "The Perfect Hacker"!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member frenzy's Avatar
    Joined
    Mar 2007
    From
    Planet Express
    Posts
    58
    how about...

    x=1001*n+422
    y=-102*n-43

    n and integer

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2007
    Posts
    18

    Thanx

    Thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Combination
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 30th 2011, 03:28 PM
  2. Linear Combination of a and b
    Posted in the Calculus Forum
    Replies: 5
    Last Post: January 21st 2011, 10:17 AM
  3. Linear Combination
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 21st 2009, 03:15 PM
  4. Linear Algebra - Linear Combination/Span
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 13th 2008, 06:06 PM
  5. Linear combination please help
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 25th 2007, 08:11 PM

Search Tags


/mathhelpforum @mathhelpforum