4-5 Matrix Inverses and Solving Systems. Warm Up Lesson Presentation Lesson Quiz
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1 Warm Up Lesson Presentation Lesson Quiz Holt Holt Algebra 2 2
2 Warm Up Find the determinant and the inverse.
3 Warm Up Find the determinant.
4 How To Find the Inverse Matrix
5 Warm Up Find the inverse.
6 1. Find the inverse of, if it exists.
7 If the determinant is 0, is undefined. So a matrix with a determinant of 0 has no inverse. It is called a singular matrix.
8 Homework Key-Solving Systems w/matrix EQ s
9 Homework Key-Matrix Inverses & Solving Systems 1. Yes, A x A -1 = A -1 x A 2. Yes, A x A -1 = A -1 x A 3. = -2, 1/-2 = 4. = -10, 1/-10 = 5. = -2, 1/-2 = 6. = -4, 1/-4 =
10 Objectives Find inverse matrices using determinants (by hand and on the calculator) Use inverse matrices to find the identity matrix Determining the equation matrix Solving systems problems using the reduced row echelon form method with the calculator
11 The matrix equation representing is shown.
12 To solve AX = B, multiply both sides by the inverse A -1. A -1 AX = A -1 B IX = A -1 B X = A -1 B The product of A -1 and A is I.
13 Check It Out! Example 3 Write the matrix equation for and solve. Step 1 Set up the matrix equation. A X = B
14 Write the matrix equation.
15 Write the matrix equation.
16 Write the matrix equation.
17 Write the matrix equation.
18 Write the system of equations for the following Jeff buys 7 apples and 4 pears for $7.25. At the same prices, Hayley buy 5 apples and 9 pears for $ What is the price of one pear? Write the matrix equation.
19 Write the system of equations for the following A total of $40,000 is invested in three money market funds m, n, and p, paying 2%, 5% and 7% simple interest, respectively. The yearly interest is $2500. Three times is invested at 2% as is invested at 5%. How much is invested in each of the funds? Write the matrix equation. =
20 Write the system of equations for the following RRHS raised $250 by selling tickets for a raffle to 54 parents and 14 students. A lucky adult will win a massage and a lucky student will win a TI-84 calculator. Parent tickets cost $4.00 more than student tickets. What are the prices of parent and student tickets. Write the matrix equation. =
21 Write the system of equations for the following The Flower Power shop is donating 200 flowers for a Mother s Day Parade float in return for their logo being prominently displayed on the float for advertising. Tyler, the Flower Power Manager ordered daises at $1.50 each, yellow roses at $5.75 each and carnations at $2.60 each. He ordered mostly daisies and 20 fewer roses than carnations. The total order came to $ How many of each type of flower was ordered. Write the matrix equation. =
22 Solving a System With Reduced Row Echelon Form 1. Define a Matrix A made from the Coefficient Matrix and the Constant Matrix 2. With your calculator, go to 2 nd x -1 and then scroll to the right to Math 3. Scroll down the menu until you see rref, (B in my menu of offerings) 4. Enter rref 5. Go back to 2 nd x -1 and enter the matrix A you defined with the Coefficient and Constant Matrices 6. Close the parentheses and hit enter 7. The values of each variable is identified with a 1 and its value in each row of a Solution Matrix
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