## Solution for problem 8 Chapter 4.2

# Solved: Let y1, y2, and y3 be defined as in Exercise 7, and let L be the linear operator

Linear Algebra with Applications | 9th Edition

Let y1, y2, and y3 be defined as in Exercise 7, and let L be the linear operator on R3 defined by L (c1y1 + c2y2 + c3y3) = (c1 + c2 + c3)y1 + (2c1 + c3)y2 (2c2 + c3)y3 (a) Find a matrix representing L with respect to the ordered basis {y1, y2, y3}. (b) For each of the following, write the vector x as a linear combination of y1, y2, and y3 and use the matrix from part (a) to determine L (x): (i) x = (7, 5, 2)T (ii) x = (3, 2, 1)T (iii) x = (1, 2, 3)T

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FIRST-ORDER SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS III: Autonomous Planar Systems David Levermore Department of Mathematics University of Maryland 4 May 2012 Because the presentation of this material in lecture will diﬀer from that in the book, I felt that notes that closely follow the lecture presentation might be appreciated. Contents 6. Autonomous Planar Systems: Integral Methods 6.1. Stationary Solutions 2 6.2. Reduction to First-Order Equations 3 6.3. Hamiltonian Systems

###### Chapter 4.2, Problem 8 is Solved

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Solved: Let y1, y2, and y3 be defined as in Exercise 7, and let L be the linear operator