MATH 3A Final: MATH3A Final Exam 2015 Fall
2
MATH 3A Full Course Notes
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{[ 1, 1, 1, 0, 0]t , [ 2, 2, 0, 1, 0]t , [ 3, 3, 0, 0, 1]t}. (b2) size of basis, 3. (b3) we use gram-schmidt with the basis from d. note that the rst 2 vectors are already orthogonal. Note that the las vector is orthogonal wrt the second vector. [ 3, 3, 0, 0, 1]t 2[ 1, 1, 1, 0, 0]t = [ 1, 1, 2, 0, 1]t . {v1 = [ 1, 1, 1, 0, 0]t , v2 = [ 2, 2, 0, 1, 0]t , v3 = [ 1, 1, 2, 0, 1]t}. 3[ 1, 1, 1, 0, 0]t , 1/3[ 2, 2, 0, 1, 0]t , 1/ {1/ (b4) we use the orthogonal basis found before (to avoid some denominators). Note that the inner product of v with the last vector in the basis is 0. We nd that the projection is equal to:
