Results 1 to 2 of 2

Math Help - Matrix- using row operations

  1. #1
    Newbie
    Joined
    Dec 2009
    From
    Fallbrook
    Posts
    18

    Matrix- using row operations

    1.) 7x + 5y - z = 94
    x + 5y + 2z = 52
    2x + y + z = 29

    Help ASAP please! thanks

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2009
    Posts
    33
    Quote Originally Posted by kelsikels View Post
    1.) 7x + 5y - z = 94
    x + 5y + 2z = 52
    2x + y + z = 29

    Help ASAP please! thanks

    Set up:

    <br />
\left(\begin{array}{ccc|c}<br />
7 & 5 & -1 & 94 \\<br />
1 & 5 & 2 & 52 \\<br />
2 & 1 & 1 & 29<br />
\end{array}\right)<br />

    Move the 2nd row to the top row. You'll see why.

    <br />
\left(\begin{array}{ccc|c}<br />
1 & 5 & 2 & 52 \\<br />
7 & 5 & -1 & 94 \\<br />
2 & 1 & 1 & 29<br />
\end{array}\right)<br />

    Take the 2nd row: subtract 7x the top row from each entry.

    <br />
\left(\begin{array}{ccc|c}<br />
1 & 5 & 2 & 52 \\<br />
0 & -30 & -15 & -270 \\<br />
2 & 1 & 1 & 29<br />
\end{array}\right)<br />

    Divide all entries in 2nd row by -15.

    <br />
\left(\begin{array}{ccc|c}<br />
1 & 5 & 2 & 52 \\<br />
0 & 2 & 1 & 18 \\<br />
2 & 1 & 1 & 29<br />
\end{array}\right)<br />

    Third row: subtract 2x the top row from each entry.

    <br />
\left(\begin{array}{ccc|c}<br />
1 & 5 & 2 & 52 \\<br />
0 & 2 & 1 & 18 \\<br />
0 & -9 & -3 & -75<br />
\end{array}\right)<br />

    Divide each entry in the 3rd row by -3.

    <br />
\left(\begin{array}{ccc|c}<br />
1 & 5 & 2 & 52 \\<br />
0 & 2 & 1 & 18 \\<br />
0 & 3 & 1 & 25<br />
\end{array}\right)<br />

    Third row: subtract 3/2x of the 2nd row.

    <br />
\left(\begin{array}{ccc|c}<br />
1 & 5 & 2 & 52 \\<br />
0 & 2 & 1 & 18 \\<br />
0 & 0 & -\frac{1}{2} & -2<br />
\end{array}\right)<br />

    Multiply the entries in the 3rd row by -2.

    <br />
\left(\begin{array}{ccc|c}<br />
1 & 5 & 2 & 52 \\<br />
0 & 2 & 1 & 18 \\<br />
0 & 0 & 1 & 4<br />
\end{array}\right)<br />

    This can be solved by back substitution, now. If you want to practice your row skills, find the answer by back substitution, then check yourself: find the answer directly by reducing it to this form:

    <br />
\left(\begin{array}{ccc|c}<br />
1 & 0& 0 & x \\<br />
0 & 1 & 0 & y \\<br />
0 & 0 & 1 & z<br />
\end{array}\right)<br />

    You might also do the steps above yourself and check my work. Maybe I tossed in a monkey wrench somewhere along the way ...?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. elementary matrix corresponding to row operations
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 30th 2010, 04:31 AM
  2. Matrix Operations
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 17th 2010, 06:44 PM
  3. Matrix Row Operations
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: November 30th 2009, 11:02 AM
  4. Replies: 17
    Last Post: August 23rd 2009, 08:25 AM
  5. Row operations on a matrix
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: June 17th 2008, 11:57 AM

Search Tags


/mathhelpforum @mathhelpforum