Consider the subset W = {(a, b,c, d) | 2b - c + 2d = 0} R4. Show that W is a sub

Question

Consider the subset W = {(a, b,c, d) | 2b - c + 2d = 0} R4. Show that W is a subspace of R4. Find a basis BW for W and state dim(W). Describe W geometrically. Show that the set S = {(1,1,0,-1)T, (-1,0,2,1)T, (1,2,2,-1)T, (1,1,2,0)T, (0.1.0. -1)T } is a spanning set for W but not a basis. Find another basis, BS, for W that consists of a selection of the vectors in S. Determine the coordinate vectors of the dependent vectors in S with respect to the ordered basis Bs found in (v). Would the set Bw {(0,2. - 1,2)T} be a basis for R4? Explain your answer.

Explanation / Answer

this is a very good question and i will answer it some later time

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