Stitz-Zeager_College_Algebra_e-book

Rewriting our system of equations we get 5625r1

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Unformatted text preview: 77, not 92. This system is 8 8 consistent dependent and its solution is 15 t + 2 , −t + 4, − 15 t + 13 , t . Our variables repre5 5 sent numbers of adults and children so they must be whole numbers. Running through the values t = 0, 1, 2, 3, 4 yields only one solution where all four variables are whole numbers; t = 3 gives us (2, 1, 1, 3). Thus there are 2 adults and 1 child in the Zahlenreichs and 1 adult and 3 kids in the Nullsatzs. 6. T (t) = 20 2 27 t − 50 9t + 60. Lowest temperature of the evening 595 12 ≈ 49.58◦ F at 12:45 AM. 476 8.3 Systems of Equations and Matrices Matrix Arithmetic In Section 8.2, we used a special class of matrices, the augmented matrices, to assist us in solving systems of linear equations. In this section, we study matrices as mathematical objects of their own accord, temporarily divorced from systems of linear equations. To do so conveniently requires some more notation. When we write A = [aij ]m×n , we mean A is an m by n matrix1 and aij is the entry found in the ith row and j th column. Schematical...
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