Answer to Question #309022 in Linear Algebra for stuti

Question #309022

Find a basis and the dimension of the subspace W of ℝ^3 where W = {( x, y, z ) ∈ ℝ^3 ∶ x + y + z = 0 }.


1
Expert's answer
2022-03-17T13:49:56-0400

From the equality x+y+z=0x+y+z=0 we find that z=(x+y)z=-(x+y). Thus, the space is 2-dimensional. To find the basis we set: x1=1,y1=0x_1=1,y_1=0 and x1=0,y1=1x_1=0,y_1=1. We receive vectors: (1,0,1)(1,0,-1) and (0,1,1)(0,1,-1). This is the basis of W.W.


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