Fredric leads a team of hikers for a full-day hike. the total elevation gain during the hike is 2,100 feet. all of the hikers have to pass two checkpoints before they reach the peak. the elevation gain from the starting point to checkpoint 1 is 100 feet less than double the elevation gain from checkpoint 2 to the peak. the elevation gain from checkpoint 1 to checkpoint 2 is the mean of the elevation gain from the start to checkpoint 1 and the elevation gain from checkpoint 2 to the peak. let x represent the elevation gain from the starting point to checkpoint 1, y represent the elevation gain from checkpoint 1 to checkpoint 2, and z represent the elevation gain from checkpoint 2 to the peak. which augmented matrices represent the context of this scenario?

1    1    1    2100

1    0   -2  -100

-1   2   -1    0

Step-by-step explanation:

x: elevation gain from the starting point to checkpoint 1 (in feet)

y: elevation gain from checkpoint 1 to checkpoint 2 (in feet)

z: elevation gain from checkpoint 2 to the peak (in feet)

The total elevation gain during the hike is 2,100 feet:

x + y + x = 2100 (eq. 1)

The elevation gain from the starting point to checkpoint 1 is 100 feet less than double the elevation gain from checkpoint 2 to the peak:

x = 2z - 100

x + 0y - 2z = - 100 (eq. 2)

The elevation gain from checkpoint 1 to checkpoint 2 is the mean of the elevation gain from the start to checkpoint 1 and the elevation gain from checkpoint 2 to the peak:

y = (x + z)/2

2y = x + z

-x +2y -z = 0 (eq. 3)

From the system of equations 1, 2 and 3 we can get the following augmented matrix:

1    1    1    2100

1    0   -2  -100

-1   2   -1    0

where the first column are the coefficients of x, the second column the coefficients of y, the third column the coefficients of z, and the last column the constants.

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step-by-step explanation: