MATH 235 Final: MATH 235 UMass Amherst final-fall06
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Fall 2006: (15 points) the matrices a and b below are row equivalent (you do not need to check this fact). 0: find a basis for the null space n ull(a) of a. 0: find a basis for the column space of a, find a basis for the row space of a, (15 points) (a) show that the characteristic polynomial of the matrix a = . Is (b) find a basis of r3 consisting of eigenvectors of a. (c) find an invertible matrix p and a diagonal matrix d such that the matrix. P 1ap = d: (15 point) i) let a be a 6 10 matrix (6 rows and 10 columns). 3 3 matrix. (a) show that each column of ab is a linear combination of the columns of a. Justify your answer: (15 points) the vectors v1 = (cid:18) 1. 1 (cid:19) are eigenvectors of the matrix a = (cid:18) . 7 . 3.
