Math 304 Quiz 1Linear AlgebraSummer 2008Instructions Please use complete sentences, along with any necessary sup-porting calculations, to answer the following questions.1. Consider the system(2x1+ x2= a26x1+ 3x2= aof simultaneous equations for the unknowns x1and x2, where a is acertain constant. For which value(s) of the constant a is the system ofequations consistent ? How do you know?May 28, 2008 Page 1 of 2 Dr. BoasMath 304 Quiz 1Linear AlgebraSummer 20082. Rose is studying the linear systemx1+ 2x2+ 3x3= 45x1+ 6x2+ 7x3= 89x1+ 10x2+ 11x3= 12(†)of three equations in the three unknowns x1, x2, and x3. Rose discov-ers that the TI-89 calculator has a command rref (which stands for“reduced row echelon form”), and the commandrref([1,2,3,4;5,6,7,8;9,10,11,12])returns the output1 0 −1 −20 1 2 30 0 0 0.What should Rose conclude about the set of solutions of the linearsystem (†)?May 28, 2008 Page 2 of 2 Dr.
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