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2.5 Determinants and Multiplicative Inverses of Matrices

2.5 Determinants and Multiplicative Inverses of Matrices. Objectives: Evaluate determinants. Find inverses of matrices. Solve systems of equations by using inverses of matrices. Page 98. 2 nd Order Determinant. Example 1 Find the value of. = 3(9) - 2(5) or 17. 3 rd Order Determinant.

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2.5 Determinants and Multiplicative Inverses of Matrices

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  1. 2.5 Determinants and Multiplicative Inverses of Matrices Objectives: Evaluate determinants. Find inverses of matrices. Solve systems of equations by using inverses of matrices. Page 98

  2. 2nd Order Determinant Example 1 Find the value of = 3(9) - 2(5) or 17

  3. 3rd Order Determinant Example 2 Find the value of + (-5) = 2 - (-3) = 2(-8) + 3(-11) – 5(-7) = -14

  4. Identity Matrix for Multiplication

  5. Inverse Matrix 2nd order

  6. Inverse Matrix 2nd order

  7. Example Solve the system of equations by using matrix equations. 3x + 2y = 3 2x – 4y = 2 Write the system as a matrix equation. To solve the matrix equation, first find the inverse of the coefficient matrix. Now multiply each side of the matrix equation by the inverse and solve. = = The solution is (1, 0).

  8. BANKING A teller at Security Bank received a deposit from a local retailer containing only twenty-dollar bills and fifty-dollar bills. He received a total of 70 bills, and the amount of the deposit was $3200. How many bills of each value were deposited? • First, let x represent the number of twenty-dollar bills and let y represent the number offifty-dollar bills. So, x + y = 70 since a total of 70 bills were deposited. • Write an equation in standard form that represents the total amount deposited. • 20x + 50y = 3,200 • Now solve the system of equations x + y = 70 and 20x + 50y = 3200. Write the system as a matrix equation and solve.

  9. = = = = The solution is (10, 60). The deposit contained 10 twenty-dollar bills and 60 fifty-dollar bills.

  10. Homework Assignment on the Internet Section2.5 (Read Determinants and Multiplicative Inverses of Matrices): Pp 102-104: 16, 18, 22, 26, 30, 32, 36, 38, 40, 46.

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