# 05-1 - 18.06 Professor Strang Quiz 1 Grading 1 Your PRINTED...

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Professor Strang Quiz 1 February 28, 2005 Grading 1 2 3 4 Your PRINTED name is: SOLUTIONS 1 (26 pts.) Suppose A is reduced by the usual row operations to R = 1 4 0 2 0 0 1 2 0 0 0 0 . Find the complete solution (if a solution exists) to this system involving the original A : Ax = sum of the columns of A. Solution The complete solution x = x particular + x nullspace has x particular = 1 1 1 1 x nullspace = x 2 - 4 1 0 0 + x 4 - 2 0 - 2 1 . The free variables x 2 and x 4 can take any values. The two special solutions came from the nullspace of R = nullspace of A . The particular solution of 1’s gives Ax = sum of the columns of A . Note : This also gives Rx = sum of columns of R . 1

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