Prac04 - THE UNIVERSITY OF SYDNEY PURE MATHEMATICS Linear Mathematics 2012 Practice session 4 1 Find a basis of the subspace V = w x y z

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Unformatted text preview: THE UNIVERSITY OF SYDNEY PURE MATHEMATICS Linear Mathematics 2012 Practice session 4 1. Find a basis of the subspace V = braceleftBigparenleftBig w x y z parenrightBig R 4 vextendsingle vextendsingle vextendsingle 2 x- y = z- 3 w bracerightBig of R 4 . 2. Let X = braceleftBigparenleftBig 1 1 1 parenrightBig , parenleftBig 1 1 parenrightBig , parenleftBig 1 parenrightBig , parenleftBig 3 2 parenrightBigbracerightBig . a ) Show that X spans R 3 . b ) Explain why X is not a basis for R 3 . c ) Find a subset of X which is a basis for R 3 . 3. You are given the following data points: x- 1 0 1 2 y 4 1- 2 1 Construct a Lagrange basis { p , p 1 , p 2 , p 3 } of P 3 using the x values from the data set. Hence find the unique cubic polynomial p ( x ) that fits the data exactly. Estimate the value of y when x = 1 2 . 4. The matrix J is a reduced row echelon form of the matrix A . Let A = parenleftbigg 1 1 3 1 0- 1 0 1 4 0 0 0 parenrightbigg ....
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This note was uploaded on 02/06/2012 for the course MATH 2061 taught by Professor Notsure during the Three '09 term at University of Sydney.

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