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assig1

# assig1 - MATH 245 Linear Algebra 2 Assignment 1 Due Wed...

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MATH 245 Linear Algebra 2, Assignment 1 Due Wed Sept 22 1: Let p = 2 1 2 - 1 , u 1 = 1 2 - 1 3 , u 2 = 3 4 1 5 , q = 1 2 - 3 0 , v 1 = 1 1 4 2 and v 2 = 1 - 2 1 - 1 . Find the point of intersection of the plane x = p + t 1 u 1 + t 2 u 2 and the plane x = q + s 1 v 1 + s 2 v 2 . 2: Let A = 2 1 4 3 2 5 3 2 5 4 3 7 1 2 - 1 3 4 - 2 2 3 0 5 6 - 1 , R = 1 0 3 0 - 1 5 0 1 - 2 0 1 - 2 0 0 0 1 1 - 1 0 0 0 0 0 0 and P = 0 1 2 - 2 - 2 1 - 1 1 1 - 1 - 1 1 1 0 4 - 3 . Given that ( A y ) is row equivalent to ( R Py ) , do the following. (a) Find a basis U for Null(A). (b) Find a matrix B such that for all x Null(A) we have [ x ] U = Bx . (c) Find a matrix C such that Col(A) = Null(C). (d) Find an invertible matrix D such that DA = R . (e) Let v 1 , v 2 , · · · , v 6 be the columns of A and let V = { v 1 , v 2 , v 4 } . Find a matrix E such that for all x Col(A) we have [ x ] V = Ex .
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