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Math Help - row operations

  1. #1
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    5 math ?'s Need Help URGENT!!!

    questions on attachment!!
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  2. #2
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    Hello, Lane!

    Here's some help . . .


    1) What is the augmented matrix for: . \begin{array}{ccc}9x + 3y  - 9z\,=\,\text{-}2 \\ 3x + 7y - 7z\,=\,6 \\ \text{-}9x - 8y - 5x\,=\,\text{-}4\end{array}
    . . \begin{pmatrix}9 & 3 & \text{-}9 & | & \text{-}2 \\ 3 & 7 & \text{-}7 & | & 6 \\ \text{-}9 & \text{-}8 & \text{-}5 & | & \text{-}4\end{pmatrix}


    2) Perform the row operation on the matrix: . \begin{pmatrix}\text{-}8 & 1 & \text{-}4 & | & 6 \\ \text{-}7 & \text{-}5 & \text{-}3 & | & 4 \\ 0 & 7 & \text{-}1 & | & 3\end{pmatrix}
    . . Multiply R_2 by 4.
    . . \begin{array}{cccc} \\ 4\!\cdot\!R_2 \\  \\ \end{array}\,\begin{pmatrix}\text{-}8 & 1 & \text{-}4 & | & 6 \\ \text{-}28 & \text{-}20 & \text{-}12 & | & 16 \\ 0 & 7 & \text{-}1 & | & 3\end{pmatrix}


    3) Perform the sequence of row operations on: . \begin{pmatrix}3 & 10 & \text{-}1 \\ 1 & 5 & \text{-}9 \\ \text{-}4 & \text{-}7 & 1\end{pmatrix}
    A: swap R_1 and R_2
    B: replace R_2 by R_2 plus \text{-}3 times  R_1
    C: replace R_3 by R_3 plus 4 times R_1
    . . \begin{array}{cccc}R_1\leftrightarrow R_2\\ \\ \\ \end{array}\,\begin{pmatrix}1 & 5 & \text{-}9 \\ 3 & 10 & \text{-}1 \\ \text{-}4 & \text{-}7 & 1\end{pmatrix}

    . . \begin{array}{cccc} \\ R_2- 3\!\cdot\!R_1 \\ \\ \end{array}\,\begin{pmatrix} 1 & 5 & \text{-}9 \\ 0 & \text{-}5 & 26 \\ \text{-}4 & \text{-}7 & 1\end{pmatrix}

    . . \begin{array}{ccc} \\ \\ R_3 + 4\!\cdot\!R_1\end{array}\,\begin{pmatrix}1 & 5 & \text{-}9 \\ 0 & \text{-}5 & 26 \\ 0 & 13 & \text{-}35\end{pmatrix}


    4) If possible, solve the system of equation using Gaussian elimination with back-substitution.

    . . \begin{array}{ccc}x + 3y + z\,=\,-12 \\ 2x + 7y - 2z \,= \,-25 \\ x - y - 6z\,=\,15\end{array}

    The determinant is \text{-}23 . . . I expect a very messy elimination.
    I'll let someone else work on it . . .



    5) If possible solve the system of equation using an inverse matrix.

    . . \begin{array}{ccc}3x + 2y - 2x\,=\,-8 \\ 3x - y - 3x\,=\,-4 \\ 6x + y - 5z\,=\,6\end{array}

    Not possible . . . the determinant is 0.

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