Suppose the system below is consistent for all possible values of f and g. What can you say about the coefficients c and d? Justify your answer.

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2x1 + 4x2 = f
cx1 + dx2 = g
asked Jan 21, 2013 in Mathematics by Nate Whidden ~Rookie~ (108 points)

1 Answer

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Put the above system in augmented matrix form and do a row reduction step. First simplifiy row one, and then subtracting c times row one into row two gives:
2   4   f                 ~          1    2    f/2               ~                 1    2    f/2      
c   d   g                             c    d    g                                    0    d-2c    g-fc/2
Looking at row 2 we see that  d-2c  =  g-fc/2.  And since the matrix is usppose to be consistent,  g-fc/2 cannot equal 0.  As a result, d-2c cannot equal 0.  And so we conclude that d cannot equal 2c
answered Jan 21, 2013 by Panda ~Expert~ (1,557 points)

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