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Perform the indicated row operations on the given augmented matrix. $\newline$ \begin{bmatrix}6 & 4 & -4 \1 & 2 & 5\end{bmatrix} $\newline$ A) Interchange row \ $2$ \ and \ row \ $1$ . $\newline$ B) Start with the matrix in your answer to part \ A. Multiply \ row \ $1$ \ by \ $-6$ \ and \ add \ the \ result \ to \ row \ $2$ . Replace \ row \ $2$ . $\newline$ $\begin{bmatrix}\Box & \Box Box & \Box\end{bmatrix}$ $\newline$ C) Start with the matrix in your answer to part \ B. Multiply \ row \ $2$ \ by \ -\frac{ $1$ }{ $8$ }. Enter \ fractional \ entries \ with \ fractions.

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One-step inequalities: word problems

Full solution

Q. Perform the indicated row operations on the given augmented matrix.

\newline

\begin{bmatrix}6 & 4 & -4 \1 & 2 & 5\end{bmatrix}

\newline

A) Interchange row \

2

\ and \ row \

1

.

\newline

B) Start with the matrix in your answer to part \ A. Multiply \ row \

1

\ by \

-6

\ and \ add \ the \ result \ to \ row \

2

. Replace \ row \

2

.

\newline

\begin{bmatrix}\Box & \Box Box & \Box\end{bmatrix}

\newline

C) Start with the matrix in your answer to part \ B. Multiply \ row \

2

\ by \ -\frac{

1

}{

8

}. Enter \ fractional \ entries \ with \ fractions.

Interchange rows: A) Interchange row $2$ and row $1$ . $\newline$ Matrix before: $\newline$ $\begin{bmatrix} 6 & 4 & -4 \\ 1 & 2 & 5 \end{bmatrix}$ $\newline$ Matrix after interchange: $\newline$ $\begin{bmatrix} 1 & 2 & 5 \\ 6 & 4 & -4 \end{bmatrix}$
Multiply and add: B) Start with the matrix in your answer to part A. Multiply row $1$ by $-6$ and add the result to row $2$ . Replace row $2$ . $\newline$ Matrix before: $\newline$ $\begin{bmatrix} 1 & 2 & 5 \\ 6 & 4 & -4 \end{bmatrix}$ $\newline$ Multiply row $1$ by $-6$ : $\newline$ $\begin{bmatrix} -6 & -12 & -30 \end{bmatrix}$ $\newline$ Add to row $2$ : $\newline$ $\begin{bmatrix} 6 & 4 & -4 \end{bmatrix} + \begin{bmatrix} -6 & -12 & -30 \end{bmatrix} = \begin{bmatrix} 0 & -8 & -34 \end{bmatrix}$ $\newline$ Matrix after operation: $\newline$ $\begin{bmatrix} 1 & 2 & 5 \\ 0 & -8 & -34 \end{bmatrix}$
Multiply row $2$ : C) Start with the matrix in your answer to part B. Multiply row $2$ by $-\frac{1}{8}$ . $\newline$ Matrix before: $\newline$ $\begin{bmatrix} 1 & 2 & 5 \\ 0 & -8 & -34 \end{bmatrix}$ $\newline$ Multiply row $2$ by $-\frac{1}{8}$ : $\newline$ $\begin{bmatrix} 0 & -8 & -34 \end{bmatrix} \times -\frac{1}{8} = \begin{bmatrix} 0 & 1 & \frac{34}{8} \end{bmatrix} = \begin{bmatrix} 0 & 1 & \frac{17}{4} \end{bmatrix}$ $\newline$ Matrix after operation: $\newline$ $\begin{bmatrix} 1 & 2 & 5 \\ 0 & 1 & \frac{17}{4} \end{bmatrix}$

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