Find a basis and the dimension of the subspace W of ℝ^3 where W = {( x, y, z ) ∈ ℝ^3 ∶ x + y + z = 0 }.
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Expert's answer
2022-03-17T13:49:56-0400
From the equality x+y+z=0 we find that z=−(x+y). Thus, the space is 2-dimensional. To find the basis we set: x1=1,y1=0 and x1=0,y1=1. We receive vectors: (1,0,−1) and (0,1,−1). This is the basis of W.
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