Consider the vectors u= 1 V= W= and let H be the subset of R4 consisting of vectors of the form x = u + rv + sw+tz with r, s, t € R. (a) If x= [1, 22, 23, 24] is in H, show that 8r+ 6s + 5t=2₁-6 2r + 2s+ t = 2₂ - 1 r+2s+ t = x3 - 1 r+ s + t = x4 - 1 (b) Put the system in part (a) in row-echelon form, where the variables in the system are r, s, t (rather than 21, 22, 23, 24). (c) Your row-echelon form will look like 0 * 00 000 Z= * #### where each is a non-zero real number, each is a real number, and each # is an expression in 21, 22, 23, 24. Use your row-echelon form to find a condition on 21, 22, 23, 24 for the system to have a solution [r, s, t], and thus find an equation of the form a121 + a222 + a3x3 + a4x4 = b defining H.

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