2.5 Determinants and Multiplicative Inverses of Matrices Objectives: 1.Evaluate determinants. 2.Find inverses of matrices. 3.Solve systems of equations.

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Presentation transcript:

2.5 Determinants and Multiplicative Inverses of Matrices Objectives: 1.Evaluate determinants. 2.Find inverses of matrices. 3.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 Example 2 Find the value of = 2 - (-3) + (-5) = 2(-8) + 3(-11) – 5(-7) = -14

Identity Matrix for Multiplication

Inverse Matrix 2 nd order

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).

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 of fifty-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 = Write the system as a matrix equation and solve.

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

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