Stitz-Zeager_College_Algebra_e-book

# Definition 815 let a be an n n matrix and cij denote

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Unformatted text preview: indeed, on the graph of y = x . This means that the graph of y = x is a hyperbola 2 − y 2 = 4 rotated counterclockwise by 45◦ .9 Below we have the graph of − it is the hyperbola x 2 x2 − y 2 = 4 (solid line) and y = x (dashed line) for comparison. y 4 3 2 1 −3 −1 −1 1 3 4 x −2 −3 When we started this section, we mentioned that we would temporarily consider matrices as their own entities, but that the algebra developed here would ultimately allow us to solve systems of linear equations. To that end, consider the system 3x − y + z = 8 x + 2y − z = 4 2x + 3y − 4z = 10 In Section 8.2, we encoded this system into the augmented matrix 3 −1 18 1 2 −1 4 2 3 −4 10 9 See Section 7.5 for more details. 488 Systems of Equations and Matrices Recall that the entries to the left of the vertical line come from the coeﬃcients of the variables in the system, while those on the right comprise the associated constants. For that reason, we may form the coeﬃcient matrix A, the unknowns matrix X and the constant matrix B as...
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