MATH 2510 HW 5

MATH 2510 HW 5 - THE CHINESE UNIVERSITY OF HONG KONG...

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Unformatted text preview: THE CHINESE UNIVERSITY OF HONG KONG Department of Mathematics MAT2310 Linear Algebra and Applications (Winter 2011) Homework 5 Due Date: 13th April 2011 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. (Optional) Let p o ( x ) , p 1 ( x ) , ··· , p n ( x ) be polynomials in P n of degrees 0 , 1 , 2 , ··· , n respectively. Show that { p o ( x ) , p 1 ( x ) , ··· , p n ( x ) } is a basis of P n . 2. (Optional) Let a , a 1 , ··· , a n be n + 1 distinct real numbers. Define polynomials p ( x ) , p 1 ( x ) , ··· , p n ( x ) by p i ( x ) = ( x − a ) ··· ( x − a i − 1 )( x − a i +1 ) ··· ( x − a n ) ( a i − a ) ··· ( a i − a i − 1 )( a i − a i +1 ) ···...
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MATH 2510 HW 5 - THE CHINESE UNIVERSITY OF HONG KONG...

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