MATH 125 Study Guide - Midterm Guide: Row Echelon Form, Gaussian Elimination, Augmented Matrix
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Note: row reduction of matrices is omitted from the solutions below. Give your answer in vector form. x1 + x2. Solution: applying the row reduction algorithm, we nd that the reduced row echelon form of the system is. The leading variables are therefore x1 and x2, and the free variables are x3 and x4. 2: let a = (2, 3) and b = ( 1, 4) be points in r2. Compute the length || ab|| of ab: let ~u, ~v be orthogonal unit vectors in rn. Compute the length ||~u + ~v|| of ~u + ~v. Solution: a) ab = [ 1 2, 4 3] = [ 3, 1], so. || ab|| = p( 3)2 + 12 = 10: to say that ~u and ~v are orthogonal unit vectors means that ||~u|| = ||~v|| = 1 and ~u ~v = 0.
