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Math Help - Solving for a solution variable in a matrix

  1. #1
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    Question Solving for a solution variable in a matrix

    The example we are given in the book is as follows:
    a1 a2 b
    1 2 -1
    -6 -5 2
    5 -18 h

    I'm assuming we put the matrix into row echelon form...making the bottom row "0 0 h" and solve for h. However, when I get to the point of calculating "-18" to "0" ... I'm having a little trouble. Can someone help me get past this final step. Thank you!
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  2. #2
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    Re: Solving for a solution variable in a matrix

    Hello, dwnicke!

    \text{The example we are given in the book is as follows: }\:\begin{bmatrix}1&2&\text{-}1 \\ \text{-}6 & \text{-}5 & 2 \\ 5 & \text{-}18 & h \end{bmatrix}

    Can you give us the original wording of the problem?

    We don't know what to "do" with that matrix.


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


    I just had a wild idea . . . bear with me.


    Suppose that matrix came from a system of equations:

    . . \begin{Bmatrix} x + 2y &=& \text{-}1 \\ \text{-}6x - 5y &=& 2 \\ 5x - 18y &=& h \end{Bmatrix}

    And the question is: "What value of h will make the system consistent?"

    The answer is: . h = 11.
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  3. #3
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    Re: Solving for a solution variable in a matrix

    The question being asked is: For what value(s) of h is b in the plane spanned by a1 and a2?

    Thank you for your help. Also, how did you get that awesome text to display matrix!?! I couldn't find it anywhere.
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  4. #4
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    Re: Solving for a solution variable in a matrix

    Soroban, I worked it out similarly to what you have done and got the same answer. Thank you again for your help.
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