Consider the subset W = {(a, b, c, d) | 2b - c + 2d = 0} R4. Show that W is a su
ID: 3103664 • Letter: C
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
I only know number 1 : that since it's in 4 variables then it's in R4