Answer:
(x, y, z) = (3, 1, 2)
Step-by-step explanation:
Solving using a calculator, I would enter the coefficients of 1/x, 1/y, 1/z as they are given. The augmented matrix in that case looks like ...
My calculator shows the solution to this set of equations to be ...
- 1/x = 1/3
- 1/y = 1
- 1/z = 1/2
So, (x, y, z) = (3, 1, 2).
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Doing this by hand, I might eliminate numerical fractions. Then the augmented matrix for equations in 1/x, 1/y, and 1/z would be ...
Adding 3 times the second row to the first, and adding the first row to the third gives ...
Then adding 14 times the first row to the third, and dividing that result by 77 yields equations that are easily solved in a couple of additional steps.
The third row tells you 3/x = 1, or x=3.
Then the second row tells you 3/3 -1/y = 0, or y=1.
Finally, the first row tells you 15/3 -4/z = 3, or z=2.