Let uˉ=⟨0,−2⟩,vˉ=⟨4,3⟩, and wˉ=⟨0,-4⟩. Find the vector xˉ that satisfies 5uˉ−vˉ+xˉ=2xˉ+wˉ In this case, xˉ=
Question
Let u̅ = ⟨0,−2⟩, v̅ = ⟨4,3⟩, and w̅ = ⟨0,-4⟩. Find the vector x̅ that satisfies 5u̅ − v̅ + x̅ = 2x̅ + w̅. In this case, x̅ =
Solution
To find the vector x, we first need to rearrange the equation to isolate x on one side. The given equation is:
5u - v + x = 2x + w
Subtract x from both sides to get:
5u - v = x + w
Then, subtract w from both sides to isolate x:
x = 5u - v - w
Now, we can substitute the given vectors into the equation:
x = 5(0, -2) - (4, 3) - (0, -4)
Perform the operations:
x = (0, -10) - (4, 3) - (0, -4)
x = (-4, -13)
So, the vector x that satisfies the equation is x = (-4, -13).
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