6.5E: Solving Systems with Gaussian Elimination (Exercises)

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Feb 8, 2022
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- 6.5: Solving Systems with Gaussian Elimination
- 7: Analytic Geometry

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For the following exercises, write the system of linear equations from the augmented matrix. Indicate whether there will be a unique solution.

51. $\left[\begin{array}{rrr|r}1 & 0 & -3 & 7 \\ 0 & 1 & 2 & -5 \\ 0 & 0 & 0 & 0\end{array}\right]$

52. $\left[\begin{array}{rrr|r}1 & 0 & 5 & -9 \\ 0 & 1 & -2 & 4 \\ 0 & 0 & 0 & 3\end{array}\right]$

For the following exercises, write the augmented matrix from the system of linear equations.

53.

$-2 x+2 y+z=7$

$2 x-8 y+5 z=0$

$19 x-10 y+22 z=3$

54.

$4 x+2 y-3 z=14$

$-12 x+3 y+z=100$

$9 x-6 y+2 z=31$

55.

$x+3 z=12$

$-x+4 y=0$

$y+2 z=-7$

For the following exercises, solve the system of linear equations using Gaussian elimination.

56.

$3 x-4 y=-7$
$-6 x+8 y=14$

$3 x-4 y=1$
$-6 x+8 y=6$

58.

$-1.1 x-2.3 y=6.2$
$-5.2 x-4.1 y=4.3$

59.

$2 x+3 y+2 z=1$

$-4 x-6 y-4 z=-2$
$10 x+15 y+10 z=0$

60.

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

$\quad 3 y+8 z=-4$
$-7 x+y+2 z=1$

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