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Unformatted text preview: UCSC MATH 21 FALL 2009 Review For Midterm 1 (1) Polynomial interpolation . The polynomial f ( x ) = c n x n + c n 1 x n 1 + ··· + c 1 x + c interpolates the points ( x 1 ,y 1 ) , ( x 2 ,y 2 ) ,..., ( x k ,y k ) if f ( x j ) = y j for j = 1 , 2 ,...,k . In other words, f ( x ) interpolates those points if its graph passes through them. Find the cubic (degree 3) polynomial that interpolates the points ( 1 , 1) , (1 , 2) , (2 , 4) and (3 , 1). Is the solution unique? Why? Hint: The equations f ( x j ) = ( y j ) give linear equations in the coefficients c ,c 1 ,...c n of the polynomial f ( x ). (2) Use GaussJordan elimination to find the reducedrowechelon form of the matrices A and B , below. A = 2 3 1 3 1 2 3 5 1 4 3 1 and B = 2 3 7 8 2 4 8 2 4 2 1 4 2 3 1 1 2 1 3 . (3) Write down the systems of equations for which the matrices A and B , in problem (2) above, are the augmented matrices. Based on your work in the problem (2), determine the solution sets formatrices....
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This note was uploaded on 03/16/2010 for the course ECON 11 taught by Professor Yk during the Spring '10 term at UCSC.
 Spring '10
 yk

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