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STATISTC 515 Midterm: STAT 515 UMass Amherst STAT515Fall2015Mid1

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turquoisegnu128
31 Jan 2019
School
UMASS-Amherst
Department
Statistics
Course
STATISTC 515
Professor
All

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Spring 2001: (4 points) let a be a 5 11 matrix (5 rows and 11 columns). Denote the rank of a by r. (a) the rank of a must be in the range. 1 (a) find the projection of b = . 0 (b) find the distance from b to w . To w : (18 points) the matrices a and b below are row equivalent (you do not need to check this fact). 3 (a) find the length of v = . Hint: let u1 be the vector in w you found in part 4d. Now nd u2 orthogonal to both w and u1: (18 points) 1 (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 a above satis es.

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