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Math Help - Augmented matrix

  1. #1
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    Post Augmented matrix

    The following matrix is obtained from a augmented matrix, system of equations.
    1 0 3 20
    0 1 2 -2
    0 0 1 4 my answer is 20,-2,4 is this right, thanks for checking my answer.
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  2. #2
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    Quote Originally Posted by kwtolley View Post
    The following matrix is obtained from a augmented matrix, system of equations.
    1 0 3 20
    0 1 2 -2
    0 0 1 4 my answer is 20,-2,4 is this right, thanks for checking my answer.
    You have:

    x_1 + 3x_3 = 20
    x_2 + 2x_3 = -2
    x_3 = 4;

    You can check yourself to see if this works.

    20 + 4(3) = 24? No.

    Get the matrix in row reduced echelon form. First, -2*Row 3 + Row 2

    = Matrix([[1, 0, 3, 20],[0, 1, 0, -10],[0, 0, 1, 4]]

    -3*Row 3 + Row 1

    = Matrix([[1, 0, 0, 8],[0, 1, 0, -10],[0, 0, 1, 4]]

    Now:

    x_1 = 8
    x_2 = -10
    x_3 = 4

    8 + 3(4) = 20? Yes.
    -10 + 2(4) = -2? Yes.
    x_3 = 4? Yes.
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  3. #3
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    Hello, kwtolley!

    You're into matrices and you still don't know how to check your answers ??
    . . Shame! .Go to your room!


    The following matrix is obtained from a augmented matrix, system of equations:

    . . \begin{vmatrix}1 & 0 &3 &|&  20 \\<br />
0 & 1& 2 &|&  \text{-}2 \\ 0& 0& 1 &|&  4\end{vmatrix}

    Most of it already reduced; we need to clear the third column only.

    \begin{array}{cccc}R_1-3R_3 \\ R_2-2R_3 \\ \\ \end{array}<br />
\begin{vmatrix}1 & 0 & 0 & | & 8 \\<br />
0 & 1 & 0 & | &\text{-}10 \\<br />
0 & 0 & 1 & | & 4 \end{vmatrix}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    The original system of equations is ridiculously simple:

    . . . . x \quad + 3z \:=\:20
    . . . . . y + 2z\:=\:\text{-}2
    . . . . . . . . . z\:=\:4

    We already have one answer: . \boxed{z \,= \,4}

    Substitute into the second equation: . y + 2(4) \:=\:\text{-}2\quad\Rightarrow\quad\boxed{y \,= \,\text{-}10}

    Substitute into the first equation: . x + 3(4)\:=\:20\quad\Rightarrow\quad\boxed{ x \,= \,8}

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  4. #4
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    Smile Thanks to you both

    Thanks again, I see where I messed up.
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