Stitz-Zeager_College_Algebra_e-book

Doing so would take advantage of the 0 there 3 1 det 0

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Unformatted text preview: −→ 4 2 0 −1 2 0 −1 4 0 −1 4 2 5 5 5 a11 b11 (2)(3) + + a12 b21 (0)(4) + + a13 b31 (−1)(5) To find R2 · C 3 where R2 denotes the second row of A and C 3 denotes the third column of B , we proceed similarly. We start with finding the product of the first entry of R2 with the first entry in C 3 then add to it the product of the second entry in R2 with the second entry in C 3, and so forth. Using entry notation, we have R2·C 3 = a21 b13 +a22 b23 +a23 b33 = (−10)(2)+(3)(−5)+(5)(−2) = −45. Schematically, 3 1 2 −8 2 0 −1 4 8 −5 9 −10 3 5 5 0 −2 −12 6 See this article on the Hadamard Product. 482 Systems of Equations and Matrices −− − − − − − − −→ −10 3 5 2 −5 −2 a21 b13 = (−10)(2) = −20 −− − − − − − − −→ −10 3 5 + 2 −5 −2 a22 b23 = (3)(−5) = −15 −− − − − − − − −→ −10 3 5 + 2 −5 −2 a23 b33 = (5)(−2) = −10 Generalizing this process, we have the following definition. Definition 8.9. Product of a Row and a Colu...
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