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# homework_5 - THE CHINESE UNIVERSITY OF HONG KONG Department...

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THE CHINESE UNIVERSITY OF HONG KONG Department of Mathematics MAT2310 Linear Algebra and Applications (Fall 2007) Homework 5 Name: Student No.: Class: Final Result: I acknowledge that I am aware of University policy and regulations on hon- esty in academic work, and of the disciplinary guidelines and procedures appli- cable to breaches of such policy and regulations, as contained in the website http://www.cuhk.edu.hk/policy/academichonesty/ Signature Date Answer all the questions. 1. Let y 1 = 1 0 0 , y 2 = 1 1 0 , y 3 = 1 1 1 , and L be the linear operator on R 3 defined by L ( c 1 y 1 + c 2 y 2 + c 3 y 3 ) = ( c 1 + c 2 + c 3 ) y 1 + (2 c 1 + c 3 ) y 2 - (2 c 2 + c 3 ) y 3 . (a) Find a matrix representing L with respect to the ordered basis [ y 1 y 2 y 3 ]. (b) Write the vector x = 1 2 3 as a linear combination of y 1 , y 2 , y 3 and use the matrix from part (a) to determine L ( x ). 2. Let L be the linear operator mapping R 3 into R 3 defined by L ( x ) = A x , where A = 3 - 1 - 2 4 0 - 4 2 - 1 - 1 and let v 1 = 2

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homework_5 - THE CHINESE UNIVERSITY OF HONG KONG Department...

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