# assign2 - Quesiton 1 (a) R = rref([A b]) R= 1.0000 0 0 S =...

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Quesiton 1 (a) R = rref([A b]) R = 1.0000 0 0 0.3305 -0.1410 0.7991 0 1.0000 0 0.2821 0.9615 0.8846 0 0 1.0000 0.6068 0.0385 -0.2179 S = rref(A) S = 1.0000 0 0 0.3305 -0.1410 0 1.0000 0 0.2821 0.9615 0 0 1.0000 0.6068 0.0385 b b = 7 9 6 A A = 9 2 9 9 1 6 5 1 4 4 0 9 9 8 9 S = R(:,1:5) S = 1.0000 0 0 0.3305 -0.1410 0 1.0000 0 0.2821 0.9615 0 0 1.0000 0.6068 0.0385 (i) Which columns of S are the pivot columns? 3 (ii) Which variables x, are the free variables? 2 (iii) What is the rank of R? 3 (iv) What is the rank of A? 3 (v) What is the nullity of A? 1 (vi) Why does the equation Ax = b have a solution? THe reason why Ax=b has a solution is b/c when you do the Gaussian reduction you find the possible solutions to the equation Ax = b. Question 1 (b) x = [R(:,6);0;0] x =

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0.7991 0.8846 -0.2179 0 0 (i) Use properties of row reduction to explain why x satisfies the equation Ax = b? THis gives you the possible solutions for the equation. When you do find the solution, A*x-b will equal to 0 because you have satisfied the solution (A*x)-b ans = 1.0e-14 * 0 0.1776 0 Question 1 (c) S = 1.0000 0 0 0.3305 -0.1410 0 1.0000 0 0.2821 0.9615 0 0 1.0000 0.6068 0.0385 u = [-S(:,4);1;0] u = -0.3305 -0.2821 -0.6068 1.0000 0 v =[-S(:,5);0;1] v = 0.1410 -0.9615 -0.0385 0 1.0000 (i) Give a handwritten explanation, using symbols and linear algebra, rather than
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## This note was uploaded on 03/19/2010 for the course MATHEMATIC 250 taught by Professor Goodman during the Spring '10 term at Rutgers.

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assign2 - Quesiton 1 (a) R = rref([A b]) R= 1.0000 0 0 S =...

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