Stitz-Zeager_College_Algebra_e-book

85 determinants and cramers rule 854 521 answers 1

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Unformatted text preview: ction, we develop the method for solving such an equation. To that end, consider the system 2x − 3y = 16 3x + 4 y = 7 To write this as a matrix equation, we follow the procedure outlined on page 488. We find the coefficient matrix A, the unknowns matrix X and constant matrix B to be 2 −3 3 4 A= X= x y B= 16 7 In order to motivate how we solve a matrix equation like AX = B , we revisit solving a similar equation involving real numbers. Consider the equation 3x = 5. To solve, we simply divide both sides by 3 and obtain x = 5 . How can we go about defining an analogous process for matrices? 3 To answer this question, we solve 3x = 5 again, but this time, we pay attention to the properties of real numbers being used at each step. Recall that dividing by 3 is the same as multiplying by 1 −1 1 3 = 3 , the so-called multiplicative inverse of 3. 3x 3−1 (3x) 3−1 · 3 x 1·x x = = = = = 5 3−1 (5) Multiply by the (multiplicative) inverse of 3 3−1 (5) Associative property of multiplication 3−1 (5) Inverse property −1 (5) 3 Multiplicative Identity If we wish to check our answer, we substitute x = 3...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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