2 5 determinants and multiplicative inverses of matrices
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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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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

2nd Order Determinant

Example 1

Find the value of

= 3(9) - 2(5) or 17


3 rd order determinant

3rd Order Determinant

Example 2

Find the value of

+ (-5)

= 2

- (-3)

= 2(-8) + 3(-11) – 5(-7)

= -14


Identity matrix for multiplication

Identity Matrix for Multiplication


Inverse matrix 2 nd order

Inverse Matrix 2nd order


Inverse matrix 2 nd order1

Inverse Matrix 2nd order


2 5 determinants and multiplicative inverses of matrices

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).


2 5 determinants and multiplicative inverses of matrices

  • 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.


2 5 determinants and multiplicative inverses of matrices

=

=

=

=

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


Homework assignment on the internet

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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