tut6 - Math 235 Tutorial 6 Problems 1: Find a and b to...

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Unformatted text preview: Math 235 Tutorial 6 Problems 1: Find a and b to obtain the best fitting equation of the form y = a + bt for the given data. t −1 1 3 . y 1 05 2: Find all least square solutions of the equation Ax = b where 110 7 1 1 0 2 1 1 0 3 A= b= , 1 0 1 6 1 0 1 5 101 4 3: Let U and W denote subspaces of a vector space V. (a) If V = U ⊕ W, define a linear mapping T : V → V by T (v ) = w where v is written uniquely as v = u + w with u ∈ U and w ∈ W. Show that ker T = U, Range(T ) = W, and T ◦ T = T . (b) Conversely, if T : V → V is a linear mapping such that T ◦ T = T , show that V = ker T ⊕ Range T . [Hint: v − T (v ) lies in ker T for all v ∈ V.] 1 ...
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This note was uploaded on 11/28/2011 for the course MATH 235 taught by Professor Celmin during the Fall '08 term at Waterloo.

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