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Past Exam for 1016 331 - Linear Algebra I at RIT (RIT)

Exam Information

Material Type:Exam 2
Professor:Staff
Class:1016 331 - Linear Algebra I
Subject:Mathematics & Statistics
University:Rochester Institute of Technology
Term: 2009
Keywords:
  • Possible Value
  • Following Matrix
  • Transformation
  • Column Space
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1016-331 RIT, 20091 1 Linear Algebra I 1016-331 Test 2 Solution 1. (6p) We know that the following matrix A has the reduced row echelon form R: A = 2 4 1 2 3 4 2 4 7 9 1 2 6 7 3 5; 2 4 1 2 0 1 0 0 1 1 0 0 0 0 3 5 = R: (a) Find a basis for row(A). The nonzero rows from R: f 1 2 0 1 ?; 0 0 1 1 ?g (b) Find a basis for col(A). The pivot columns from A: f 2 4 1 2 1 3 5; 2 4 3 7 6 3 5g (c) Find a basis for null(A). We solve the system given by Ax = 0: if the variables are x;y;z and u, then from R we see that y and u are free and z = u and x = u2y. This means that the solutions are 2 66 4 x y z u 3 77 5 = 2 66 4 u2y y u u 3 77 5: This shows that the answer is f 2 66 4 2 1 0 0 3 77 5; 2 66 4 1 0 1 1 3 77 5g 1016-331 RIT, 20091 2 2. (6p) Find the dimension of spanf 2 66 4 1 2 3 4 3 77 5; 2 66 4 2 4 7 9 3 77 5; 2 66 4 1 2 6 7 3 77 5g: This span is just the row space of the previo...
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