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Stitz-Zeager_College_Algebra_e-book

# For example if a is a 2 3 matrix and b is a 3 2

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Unformatted text preview: he contributed volumes of the two stock solutions and the water. That is amount of 30% stock solution + amount of 90% stock solution + amount of water = 500 mL Using our deﬁned variables, this reduces to x + y + w = 500. Next, we need to make sure the ﬁnal solution is 40% acid. Since water contains no acid, the acid will come from the stock solutions only. We ﬁnd 40% of 500 mL to be 200 mL which means the ﬁnal solution must contain 200 mL of acid. We have amount of acid in 30% stock solution + amount of acid 90% stock solution = 200 mL The amount of acid in x mL of 30% stock is 0.30x and the amount of acid in y mL of 90% solution is 0.90y . We have 0.30x + 0.90y = 200. Converting to fractions,14 our system of equations becomes x + y + w = 500 9 3 10 x + 10 y = 200 We ﬁrst eliminate the x from the second equation (E 1) x + y + w = 500 3 9 (E 2) 10 x + 10 y = 200 Replace E 2 with − 3 E1 + E2 −−−−−−−−−→ − − − − − −10 − − − (E 1) x + y + w = 500 3 3 (E 2) 5 y − 10 w = 50 Next, we get a coeﬃcien...
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