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

**Chapter 4, Problem 8**

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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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