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## Homework Statement

Use the Gram-Schmidt algorithm to convert the set S={x

_{1}, x

_{2}, x

_{3}} to an orthagonal set, given x

_{1 = [1 1 1 1]T, x2 = [6 0 0 2]T, x3 = [-1 -1 2 4]T. Homework Equations The Attempt at a Solution I've used the algorithm to come up with the set of vectors {[1 1 1 1]T, [-2 -2 1 3]T, [10/3 -8/3 -5/3 3]T. I've triple checked that I have executed the algorithm correctly. My first two vectors are orthagonal; their dot product is zero. The dot product of third vector with either of the other two vectors is non-zero. Is this an orthagonal set? By definition I'm assuming that it's not, but is there some way that a set of 3 vectors in R4 can be orthagonal without all three vectors themselves being orthagonal... ? I highly doubt it.. but can someone provide some insight? Thank you}