1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Matrix-Vector Form Write an Augmented Matrix

  1. Feb 11, 2016 #1
    1. The problem statement, all variables and given/known data
    Write in Vector-Matrix form then write the augmented matrix of the system.
    r + 2s + t = 1
    r - 3s +3t = 1
    4s - 5t = 3

    2. Relevant equations
    The matrix to which the operations will be applied is called the augmented matrix of the system Ax = b, It is formed by appending the entries of the column vector b (right hand side of the equation) to those of the coefficient matrix A, creating a matrix that is now of order m x (n + 1).

    3. The attempt at a solution
    I know to use the coefficients to build the rows and columns of a 3 x 3 (?) matrix but I don't understand the augmentation part.
     
    Last edited: Feb 11, 2016
  2. jcsd
  3. Feb 11, 2016 #2

    Mark44

    Staff: Mentor

    The last bit makes no sense. If matrix A is m x n (m rows by n columns), the augmented matrix will be m x (n + 1), NOT m x (n + 1)^4.
    The constants on the right sides of the three equations will be the 4th column of the augmented 3 x 4 matrix.
     
  4. Feb 11, 2016 #3
    Okay, so you have these linear equations:
    \begin{array}{lcl}
    r + 2s + t & = & 1 \\
    r - 3s + 3t & = & 1 \\
    4s - 5t & = & 3 \end{array}​
    Now, you said you know how to make them into a matrix. The augmentation part is actually really easy. All you have to do is add the answers to the last column.
    \begin{array}{ccc}
    1 & 2 & 1 & 1\\
    1 & -3 & 3 & 1 \\
    0 & 4 & -5 & 3\end{array}​
    It is common to see a dotted line separating the fourth column from the 3x3 matrix.
     
  5. Feb 11, 2016 #4
    1.) THE 4 WAS A MISTAKE IT WAS AN INDEX FOR THE FOOTNOTE: "The optional vertical line between the entries of A and those of b emphasizes the way the matrix is constructed"
     
    Last edited: Feb 11, 2016
  6. Feb 11, 2016 #5
    Cool thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Matrix-Vector Form Write an Augmented Matrix
  1. Matrix ? (Replies: 4)

  2. Matrix vector subspace (Replies: 10)

Loading...