Consistent ?? Think again
⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧ x 1 + x 3 = 1 − x 2 + 2 x 3 = ω x 1 − x 2 + 3 x 3 = 2 x 1 + x 2 − x 3 = 1 − ω
Consider the linear systems above, where ω is an arbitrary real constant.
Determine the value(s) of ω that results in a consistent system.
Note : If there's more than one value of ω , then submit their sum as your answer.
The answer is 1.
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Subtracting equation 1 from equation 3 we get, − x 2 + 2 x 3 = 1
From equation 2 we get, − x 2 + 2 x 3 = w
So, w = 1