Results 1 to 4 of 4

Thread: Vectors

  1. #1
    Senior Member
    Joined
    Nov 2008
    Posts
    425

    Vectors

    If a = 3x+2y and b=5x-4y, find x and y in terms of a and b.

    Note: bolded=vectors (arrows on top)

    So this is my attempt, but leads me to no enlightenment.. Please demonstrate to me the method to proceed to the correct answer.

    x = (a/3) - (2y/3)
    y = (-b/4) +(5x/4)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,216
    Thanks
    3702
    Quote Originally Posted by skeske1234 View Post
    If a = 3x+2y and b=5x-4y, find x and y in terms of a and b.

    Note: bolded=vectors (arrows on top)

    So this is my attempt, but leads me to no enlightenment.. Please demonstrate to me the method to proceed to the correct answer.

    x = (a/3) - (2y/3)
    y = (-b/4) +(5x/4)
    $\displaystyle 2\vec{a} = 6\vec{x} + 4\vec{y}$

    $\displaystyle \vec{b} = 5\vec{x} - 4\vec{y}$

    ------------------------------------------------ add em' up ...

    $\displaystyle 2\vec{a} + \vec{b} = 11\vec{x}$

    solve for vector x ...

    $\displaystyle \vec{x} = \frac{2}{11} \vec{a} + \frac{1}{11} \vec{b} $
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Mauritzvdworm's Avatar
    Joined
    Aug 2009
    From
    Pretoria
    Posts
    122
    equation 1: $\displaystyle \overline{a}=3\overline{x}+2\overline{y}$
    equation 2: $\displaystyle \overline{b}=5\overline{x}-4\overline{y}$

    multiply equation 1 by 2 and add the result to the second equation

    $\displaystyle 2\overline{a}+\overline{b}=11\overline{x}$
    hence, solving for x we obtain
    $\displaystyle \overline{x}=\frac{1}{11}(2\overline{a}+\overline{ b})$

    to solve for $\displaystyle \overline{y}$ we need to multiply the first equation by 5 and the second by 3 then subtract the second from the first, we obtain

    $\displaystyle 5\overline{a}-3\overline{b}=22\overline{y}$
    solving for y we find
    $\displaystyle \overline{y}=\frac{1}{22}(5\overline{a}-3\overline{b})$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,782
    Thanks
    2824
    Awards
    1
    Quote Originally Posted by skeske1234 View Post
    If a = 3x+2y and b=5x-4y, find x and y in terms of a and b.
    We can write this in matrix form: $\displaystyle \left[ \begin{gathered}
    a \hfill \\
    b \hfill \\
    \end{gathered} \right] = \left[ {\begin{array}{rr}
    3 & 2 \\
    5 & { - 4} \\
    \end{array} } \right]\left[ \begin{gathered}
    x \hfill \\
    y \hfill \\
    \end{gathered} \right]$

    So $\displaystyle \left[ \begin{gathered}
    x \hfill \\
    y \hfill \\
    \end{gathered} \right] = \left[ {\begin{array}{rr}
    {\frac{2}
    {{11}}} & {\frac{1}
    {{11}}} \\
    {\frac{5}
    {{22}}} & {\frac{{ - 3}}
    {{22}}} \\
    \end{array} } \right]\left[ \begin{gathered}
    a \hfill \\
    b \hfill \\
    \end{gathered} \right]$
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: Nov 15th 2011, 05:10 PM
  2. Replies: 3
    Last Post: Jun 30th 2011, 08:05 PM
  3. Replies: 2
    Last Post: Jun 18th 2011, 10:31 AM
  4. [SOLVED] Vectors: Finding coefficients to scalars with given vectors.
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Jan 23rd 2011, 12:47 AM
  5. Replies: 4
    Last Post: May 10th 2009, 06:03 PM

Search Tags


/mathhelpforum @mathhelpforum