Question

6. Solve each of the following systems by Gaussian elimination. (a) \[ \begin{array}{l} 3 x+2 y-z=-15 \\ 5 x+3 y+2 z=0 \\ 3 x+y+3 z=11 \\ -6 x-4 y+2 z=30 \end{array} \] (b) \[ \begin{array}{l} w+2 x-y=4 \\ x-y=3 \\ w+3 x-2 y=7 \\ 2 u+4 v+w+7 x=7 \end{array} \] (c) \[ \begin{array}{l} 10 y-4 z+w=1 \\ x+4 y-z+w=2 \\ 3 x+2 y+z+2 w=5 \\ -2 x-8 y+2 z-2 w=-4 \\ x-6 y+3 z=1 \end{array} \] (d) \[ \begin{array}{l} y-z+2 w=0 \\ 3 x+2 y+w=0 \\ 2 x+4 w=12 \\ -2 x-2 z+5 w=6 \end{array} \]

          6. Solve each of the following systems by Gaussian elimination.
(a)
\[
\begin{array}{l}
3 x+2 y-z=-15 \\
5 x+3 y+2 z=0 \\
3 x+y+3 z=11 \\
-6 x-4 y+2 z=30
\end{array}
\]
(b)
\[
\begin{array}{l}
w+2 x-y=4 \\
x-y=3 \\
w+3 x-2 y=7 \\
2 u+4 v+w+7 x=7
\end{array}
\]
(c)
\[
\begin{array}{l}
10 y-4 z+w=1 \\
x+4 y-z+w=2 \\
3 x+2 y+z+2 w=5 \\
-2 x-8 y+2 z-2 w=-4 \\
x-6 y+3 z=1
\end{array}
\]
(d)
\[
\begin{array}{l}
y-z+2 w=0 \\
3 x+2 y+w=0 \\
2 x+4 w=12 \\
-2 x-2 z+5 w=6
\end{array}
\]

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6. Solve each of the following systems by Gaussian elimination.
(a)

3 x+2 y-z=-15

5 x+3 y+2 z=0

3 x+y+3 z=11

-6 x-4 y+2 z=30

(b)

w+2 x-y=4

x-y=3

w+3 x-2 y=7

2 u+4 v+w+7 x=7

(c)

10 y-4 z+w=1

x+4 y-z+w=2

3 x+2 y+z+2 w=5

-2 x-8 y+2 z-2 w=-4

x-6 y+3 z=1

(d)

y-z+2 w=0

3 x+2 y+w=0

2 x+4 w=12

-2 x-2 z+5 w=6

Added by Erica G.

College Algebra and Trigonometry

Margaret L. Lial, John Hornsby, David I.… 7th Edition

Chapter 9

Instant Answer

Solved by Expert Deann Nicolaus

07/23/2024

Step 1

Step 1: For system (a), write the augmented matrix for the system of equations: \[ \begin{array}{ccc|c} 3 & 2 & -1 & -15 \\ 5 & 3 & 2 & 0 \\ 3 & 1 & 3 & 11 \\ -6 & -4 & 2 & 30 \\ \end{array} \] Show more…

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6. Solve each of the following systems by Gaussian elimination. (a) \[ \begin{array}{l} 3 x+2 y-z=-15 \\ 5 x+3 y+2 z=0 \\ 3 x+y+3 z=11 \\ -6 x-4 y+2 z=30 \end{array} \] (b) \[ \begin{array}{l} w+2 x-y=4 \\ x-y=3 \\ w+3 x-2 y=7 \\ 2 u+4 v+w+7 x=7 \end{array} \] (c) \[ \begin{array}{l} 10 y-4 z+w=1 \\ x+4 y-z+w=2 \\ 3 x+2 y+z+2 w=5 \\ -2 x-8 y+2 z-2 w=-4 \\ x-6 y+3 z=1 \end{array} \] (d) \[ \begin{array}{l} y-z+2 w=0 \\ 3 x+2 y+w=0 \\ 2 x+4 w=12 \\ -2 x-2 z+5 w=6 \end{array} \]

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