How is w=(3,5,1)∈R
3
a linear combination of u=(0,−2,2)
and v=(1,3,−1)
?
w is a linear combination of u and v if exist such x and y so x*u +y*v = w
That means that
Or
From the fist equation find that y = 3, and substitute it in the last equation get 2x -3 = 1, or x = 2. After substituting x=2 and y=3 in the second equation confirmed it is satisfied.
So w = 2*u + 3*v
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