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Math Help - consistent linear equations

  1. #1
    Junior Member
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    consistent linear equations

    If you have matrix 2,-3,h
    -6 9 5, and you want a value for h so that this matrix is of a consistent linear equation, then what is the value for h?

    My answer is that the system of equations is inconsistent no matter what the value of h is.
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  2. #2
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    Hello, lord12

    If you have matrix: . \begin{bmatrix}2 &\text{-}3 &h \\ \text{-}6 & 9 & 5\end{bmatrix} and you want a value for h

    so that this matrix is of a consistent linear equation, then what is the value for h ?

    We have: . \left[\begin{array}{cc|c} 2 & \text{-}3 & h \\ \text{-}6 & 9 & 5 \end{array}\right]

    \begin{array}{c}\\ R_3 + 3R_1\end{array}\left[\begin{array}{cc|c} 2 & \text{-}3 & h \\ 0 & 0 & 3h+5 \end{array}\right]


    If 3h+5 \:\neq\:0, the system is inconsistent.


    If 3h+5\:=\:0 \quad\Rightarrow\quad h \:=\:-\tfrac{5}{3}, the system is consistent.
    . . And there is an infinite number of solutions.


    The solutions are: . \begin{array}{c}x \:=\:\frac{3}{2}t + \frac{h}{2} \\ y \:=\:t \end{array} \quad\hdots for any value of t.

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