Write the vector w = (1,1) as a linear combination of the vectors u = (2,1) and v= (2, 2) in R^2. Write the vector d= (2,0,1) as a linear combination of the vectors a= (3,1,2), b = (1,1,1), and c=(7,3,5) in R³.
Added by Jesus M.
Step 1
We want to find scalars x and y such that: w = x * u + y * v (1,1) = x * (2,1) + y * (2,2) Now, we can write this as a system of linear equations: 2x + 2y = 1 x + 2y = 1 We can solve this system by subtracting the second equation from the first: x = 0 Now, Show more…
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