Asked by Yissel Galarza on May 15, 2024
Verified
Write the system of linear equations represented by the augmented matrix below. Use variables x , y , z , v , and w.
[−4−6−77−9−4−3−3−79−2−1−57−2−7−7−7−73]\left[ \begin{array} { c c c c : c } - 4 & - 6 & - 7 & 7 & - 9 \\- 4 & - 3 & - 3 & - 7 & 9 \\- 2 & - 1 & - 5 & 7 & - 2 \\- 7 & - 7 & - 7 & - 7 & 3\end{array} \right]−4−4−2−7−6−3−1−7−7−3−5−77−77−7−99−23
A) {−4x−6y−7z+7w=−9−4x−3y−3z−7w=9−2x−y−5z+7w=−2−7x−7y−7z−7w=3\left\{ \begin{array} { l } - 4 x - 6 y - 7 z + 7 w = - 9 \\- 4 x - 3 y - 3 z - 7 w = 9 \\- 2 x - y - 5 z + 7 w = - 2 \\- 7 x - 7 y - 7 z - 7 w = 3\end{array} \right.⎩⎨⎧−4x−6y−7z+7w=−9−4x−3y−3z−7w=9−2x−y−5z+7w=−2−7x−7y−7z−7w=3
B) {−4x−6y−7z+7w=−16−4x−3y−3z−7w=6−2x−y−5z+7w=−7−7x−7y−7z−7w=10\left\{ \begin{array} { l } - 4 x - 6 y - 7 z + 7 w = - 16 \\- 4 x - 3 y - 3 z - 7 w = 6 \\- 2 x - y - 5 z + 7 w = - 7 \\- 7 x - 7 y - 7 z - 7 w = 10\end{array} \right.⎩⎨⎧−4x−6y−7z+7w=−16−4x−3y−3z−7w=6−2x−y−5z+7w=−7−7x−7y−7z−7w=10
C) {−4x−6y−7z+7w−9=0−4x−3y−3z−7w+9=0−2x−y−5z+7w−2=0−7x−7y−7z−7w+3=0\left\{ \begin{array} { r } - 4 x - 6 y - 7 z + 7 w - 9 = 0 \\- 4 x - 3 y - 3 z - 7 w + 9 = 0 \\- 2 x - y - 5 z + 7 w - 2 = 0 \\- 7 x - 7 y - 7 z - 7 w + 3 = 0\end{array} \right.⎩⎨⎧−4x−6y−7z+7w−9=0−4x−3y−3z−7w+9=0−2x−y−5z+7w−2=0−7x−7y−7z−7w+3=0
D) {−4x−6y−7z=−9−4x−3y−3z=9−2x−y−5z=−2−7x−7y−7z=3\left\{ \begin{array} { l } - 4 x - 6 y - 7 z = - 9 \\- 4 x - 3 y - 3 z = 9 \\- 2 x - y - 5 z = - 2 \\- 7 x - 7 y - 7 z = 3\end{array} \right.⎩⎨⎧−4x−6y−7z=−9−4x−3y−3z=9−2x−y−5z=−2−7x−7y−7z=3
E) {−4x−6y−7z+7w=0−4x−3y−3z−7w=0−2x−y−5z+7w=0−7x−7y−7z−7w=0\left\{ \begin{array} { r } - 4 x - 6 y - 7 z + 7 w = 0 \\- 4 x - 3 y - 3 z - 7 w = 0 \\- 2 x - y - 5 z + 7 w = 0 \\- 7 x - 7 y - 7 z - 7 w = 0\end{array} \right.⎩⎨⎧−4x−6y−7z+7w=0−4x−3y−3z−7w=0−2x−y−5z+7w=0−7x−7y−7z−7w=0
Augmented Matrix
A matrix obtained by appending the columns of two given matrices, typically representing a system of linear equations.
Linear Equations
Equations between two variables that give a straight line when plotted on a graph.
- Understand and address challenges through the application of matrix notation and operations.
Verified Answer
MB
Miyara ButlerMay 19, 2024
Final Answer :
A
Explanation :
The system of linear equations represented by the augmented matrix [−4−6−77−9−4−3−3−79−2−1−57−2−7−7−7−73]\left[ \begin{array} { c c c c : c } - 4 & - 6 & - 7 & 7 & - 9 \\- 4 & - 3 & - 3 & - 7 & 9 \\- 2 & - 1 & - 5 & 7 & - 2 \\- 7 & - 7 & - 7 & - 7 & 3\end{array} \right]−4−4−2−7−6−3−1−7−7−3−5−77−77−7−99−23 is given by {−4x−6y−7z+7w=−9−4x−3y−3z−7w=9−2x−y−5z+7w=−2−7x−7y−7z−7w=3\left\{ \begin{array} { l } - 4 x - 6 y - 7 z + 7 w = - 9 \\- 4 x - 3 y - 3 z - 7 w = 9 \\- 2 x - y - 5 z + 7 w = - 2 \\- 7 x - 7 y - 7 z - 7 w = 3\end{array} \right.⎩⎨⎧−4x−6y−7z+7w=−9−4x−3y−3z−7w=9−2x−y−5z+7w=−2−7x−7y−7z−7w=3 . All the other answer choices are either missing some constants or have incorrect constants.
Learning Objectives
- Understand and address challenges through the application of matrix notation and operations.
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