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Unformatted text preview: 77, not 92. This system is
consistent dependent and its solution is 15 t + 2 , −t + 4, − 15 t + 13 , t . Our variables repre5
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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