Can you solve this using matrices by row operations 4x+y-2z=-6 2x-3y+3z=9 x-2y=0

Question

Can you solve this using matrices by row operations
4x+y-2z=-6
2x-3y+3z=9
x-2y=0

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Answers ( No )

    0
    2021-09-19T05:23:24+00:00

    Answer:

    (x, y, z) = (0, 0, 3)

    Step-by-step explanation:

    The augmented matrix for the system is …

    \left[\begin{array}{cccc}4&1&-2&-6\\2&-3&3&9\\1&-2&0&0\end{array}\right]

    Subtract 4 times the 3rd row from the first row.

    \left[\begin{array}{cccc}0&9&-2&-6\\2&-3&3&9\\1&-2&0&0\end{array}\right]

    Subtract 2 times the 3rd row from the second row.

    \left[\begin{array}{cccc}0&9&-2&-6\\0&1&3&9\\1&-2&0&0\end{array}\right]

    Subtract 9 times the 2nd row from the first row.

    \left[\begin{array}{cccc}0&0&-29&-87\\0&1&3&9\\1&-2&0&0\end{array}\right]

    Now, the first row can be divided by -29 to give …

    \left[\begin{array}{cccc}0&0&1&3\\0&1&3&9\\1&-2&0&0\end{array}\right]

    You can subtract 3 times this first row from the second row to get …

    \left[\begin{array}{cccc}0&0&1&3\\0&1&0&0\\1&-2&0&0\end{array}\right]

    And add 2 times the second row to the third to get …

    \left[\begin{array}{cccc}0&0&1&3\\0&1&0&0\\1&0&0&0\end{array}\right]

    This matrix now tells you (x, y, z) = (0, 0, 3).

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