792 CHAPTER 11 Systems of Equations and Inequalities Demonstrating Theorem (15) ( ) = − = − = − = − = − = k k k k k k k 1 2 4 6 6 8 2 2 4 6 6 8 2 2 1 2 4 6 EXAMPLE 8 THEOREM If the entries of any row (or any column) of a determinant are multiplied by a nonzero number k and the result is added to the corresponding entries of another row (or column), the value of the determinant remains unchanged. (16) Now Work PROBLEM 45 Demonstrating Theorem (16) = − → − = − 3 4 5 2 14 3 4 5 2 7 0 5 2 14 ↑ Multiply row 2 by −2 and add to row 1. EXAMPLE 9 11.3 Assess Your Understanding In Problem 69, you are asked to prove the theorem for a 3 by 3 determinant using rows 1 and 2. 4. True or False When using Cramer’s Rule, if = D 0, then the system of linear equations is inconsistent. 5. True or False If any row (or any column) of a determinant is multiplied by a nonzero number k, the value of the determinant remains unchanged. 6. Multiple Choice If any two rows of a determinant are interchanged, its value: (a) changes sign (b) becomes zero (c) remains the same (d) no longer relates to the original value 1. = = D a b c d . 2. Using Cramer’s Rule, the value of x that satisfies the system of equations + = − =− ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ x y x y 2 3 5 4 3 is x 2 3 1 4 . = − 3. True or False A determinant can never equal 0. Concepts and Vocabulary Skill Building In Problems 7–14, find the value of each determinant. 7. − 6 4 1 3 8. − 8 3 4 2 9. − − 3 1 4 2 10. − − 4 2 5 3 11. 3 4 2 1 1 5 1 2 2 − − 12. 1 3 2 6 1 5 8 2 3 − − 13. 4 1 2 6 1 0 1 3 4 − − − 14. 3 9 4 1 4 0 8 3 1 − − 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
RkJQdWJsaXNoZXIy NjM5ODQ=