Results 1 to 3 of 3

Math Help - solving a matrix equation for a,b,c, and d

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    42

    solving a matrix equation for a,b,c, and d

    [a-b b+c] = [8 1]
    [3d+c 2a-4d] [7 6]



    I know that since the matrices are equal:

    a-b=8
    b+c=1
    3d+c=7
    2a-4d=6

    but not sure where to go from here
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    Quote Originally Posted by cottekr View Post
    [a-b b+c] = [8 1]
    [3d+c 2a-4d] [7 6]



    I know that since the matrices are equal:

    a-b=8
    b+c=1
    3d+c=7
    2a-4d=6

    but not sure where to go from here
    You have made a good start.

    From the first equation a = 8+b

    From the second c = 1-b

    From the third (and second) d = \frac{7-c}{3} \implies  \frac{7-(1-b)}{3} = \frac{6+b}{3}

    Now looking at the 4th equation 2a-4d=6 we have new information for a and d so lets use it in the 4th.

     <br />
2a-4d=6\implies 2(8+b)-4\left(\frac{6+b}{3}\right)=6<br />

    Now expand and solve for b
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2009
    Posts
    153
    <br />
A\begin{bmatrix}a\\b\\c\\d\end{bmatrix}= \begin{bmatrix}a-b\\b+c\\3d+c\\2a-4d\end{bmatrix}=<br />
 a\begin{bmatrix}1\\0\\0\\2\end{bmatrix}+<br />
 b\begin{bmatrix}-1\\1\\0\\0\end{bmatrix}+<br />
 c\begin{bmatrix}0\\1\\1\\0\end{bmatrix}+<br />
 d\begin{bmatrix}0\\0\\3\\-4\end{bmatrix} \\<br />

    <br />
 =\begin{bmatrix}<br />
 1 &-1 &0 &0 \\<br />
 0 &1 &1 &0 \\<br />
 0 &0 &1 &3 \\<br />
 2 &0 &0 &-4 \\<br />
 \end{bmatrix}<br />
 \begin{bmatrix}a\\b\\c\\d\end{bmatrix}=<br />
 \begin{bmatrix}8\\1\\7\\6\end{bmatrix}~,~<br />
 \begin{bmatrix}a\\b\\c\\d\end{bmatrix}=<br />
 A^{-1}\begin{bmatrix}8\\1\\7\\6\end{bmatrix}=<br />
 \begin{bmatrix}5\\-3\\4\\1\end{bmatrix}<br /> <br />
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solving for a Matrix
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: September 7th 2011, 09:19 PM
  2. Help in solving a following matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 26th 2011, 08:58 AM
  3. Solving for x, y, z, w in a matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 21st 2010, 01:09 PM
  4. solving the matrix equation
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 25th 2010, 10:21 AM
  5. Replies: 1
    Last Post: November 20th 2007, 11:50 PM

Search Tags


/mathhelpforum @mathhelpforum