MATH 235 Midterm: MATH 235 UMass Amherst exam1-fall06
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Fall 2001: (16 points) the matrices a and b below are row equivalent (you do not need to check this fact). 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 a above satis es. P 1ap = d: (4 point) let a be a 6 10 matrix (6 rows and 10 columns). Denote the dimension of the column space of a by r. (a) the dimension r of the column space must be in the range. 3 . 7 (cid:19). (a) the eigenvalue of v1 is. 2 (cid:19) in the basis {v1, v2}. (b) find the coordinates of (cid:18) 1 (c) compute a100(cid:18) 1 (d) as n gets larger, the vector an(cid:18) 1. Justify your answer: (16 points) let w be the plane in r3 spanned by u1 = .
