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Stitz-Zeager_College_Algebra_e-book

If we let tdown denote the time of the downstream

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Unformatted text preview: ltimate sign of the term in the expansion of the determinant. To illustrate some of the other properties in Theorem 8.7, we use row operations to transform our 3 × 3 matrix A into an upper triangular matrix, keeping track of the row operations, and labeling 2 For a very elegant treatment, take a course in Linear Algebra. There, you will most likely see the treatment of determinants logically reversed than what is presented here. Speciﬁcally, the determinant is deﬁned as a function which takes a square matrix to a real number and satisﬁes some of the properties in Theorem 8.7. From that function, a formula for the determinant is developed. 512 Systems of Equations and Matrices each successive matrix.3 3 1 0 −1 2 1 A 2 3 1 Replace R3 5 − − − − − → 0 −1 −−−−− with − 2 R1 + R3 1 3 4 0 3 B 2 3 1 Replace R3 with 5 − − − − − → 0 −1 −−−−− 1 R2 + R3 8 3 0 0 3 C 2 5 13 3 Theorem 8.7 guarantees us that det(A) = det(B ) = det(C ) since we are replacing a row with itself plus a mu...
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