MATH 232 Final: MATH232 MATH232 FinalC
31 Jan 2019
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Page 1 of 14: consider the plane in r3 that goes through the point (2, 1, 3) and is perpendicular to the vector (1, 1, 1). [3] (a) give a general equation of this plane. [3] (b) give a vector equation of this plane. Page 2 of 14: consider the matrix a = . [4] (a) find elementary matrices e1 and e2 such that e2e1a = i. [2] (b) write a 1 as a product of two elementary matrices. [3] (c) write a as a product of two elementary matrices. Page 3 of 14: let w1 = (1, 1, 0, 1), w2 = ( 1, 1, 0, 0), w3 = (1, 2, 0, 0). [4] (a) use the gram-schmidt process to obtain an orthogonal basis {v1, v2, v3} for w . [5: let a and b be two square matrices of the same size.
