# X y z w 3 3 x 2 z 5 w 11 2 y z 1 4 x 5 y 3 w 4 c 2 x

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6. Consider the following system of linear equations-x-3y=-33x+9y=k.(a) For what values ofkwill the system have no solution?(b) For what values ofkwill the system have infinitely many solutions?7. LetA=25-1374-316,B=1-2-3854,C=-409.(a) Write down the sizes of the matricesA,B, andC. Use this to decide which of thesix productsAB,BA,AC,CA,BC,CBare defined.(b) Calculate the products that are defined in part (a).8. The distributive law says that (A+B)C=AC+BC. That is, addingAandBandthen multiplying on the right byCgives the same results as first multiplying each ofAandBon the right byCand then adding. Verify the distributive law for the givenmatrices.A=1203,B=3-254,C=619. A store sells three types of MP3 players.MatrixAcontains information about size(in gigabytes), battery life (in hours, and weight (in ounces) of the three MP3 players.MatrixBcontains the sale prices (in dollars) of the MP3 players, while matrixCcontainsthe number of each type of player sold in one week.
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