MATH 551 Midterm: MATH 551 KSU Test 2u01

• School: Kansas State University
• Department: Mathematics
• Course: MATH 551
• Professor: All

Document Summary

July 23, 2001: given that the eigenvalues of the matrix a are = 2, 1 nd (if possible) a basis. As a linear combination of of eigenvectors. 0 eigenvectors and use this to compute a3x. 1: find the eigenvalues and a basis of eigenvectors for the following matrix b; nd a diag- onal matrix d and an invertible matrix q so that b = qdq 1. B = (cid:20) 1 1: compute (show your work!) det a using row reduction. 7 4 0 3: show that the following vectors form an orthogonal basis for r3. Find the coordinate vectors of x = . With respect to this basis: find all possible 2 2 matrices with eigenvalues 1, 2 and corresponding eigenvectors. 3: please answer true or false to each of the following questions. A correct answer without explanation will receive only half credit. (a) the following matrix is orthogonal.