Determinants WKST 2112022 3 10 AM 3 7
- Slides: 28
Determinants WKST 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 1
Cramer’s Rule section 4. 4 dangjim@gmail. com Revised © 2011 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 2
For Your Information • Named by Gabriel Cramer in 1700’s • Uses determinant to find solution of the system – Revisit the formula of the determinant for 2 x 2 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 3
Recall Equation of a determinant (NOT THE INVERSE): After Death – Before Christ 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 4
Steps A. Find the determinant B. To get x: 1. Write in determinant form (without the equal sign) 2. REPLACE the x-coordinates with the numbers associated after the equal sign 3. Divide it by the determinant C. To get y: 1. Same process as x but replace it with the y-coordinate D. Write the answer as an ordered pair 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 5
Equations To get x: D = Determinant Equation: To get y: . 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 6
Example 1 Use Cramer’s Rule to determine this system: What is the determinant? 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 7
Example 1 Use Cramer’s Rule to determine this system: First, setup the X solution 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 8
Example 1 Use Cramer’s Rule to determine this system: First, setup the X solution To get X, get rid of the coefficients in front of X and replace them with the answers 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 9
Example 1 Use Cramer’s Rule to determine this system: Solve for X. 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 10
Example 1 Use Cramer’s Rule to determine this system: Solve for X. 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 11
Example 1 Use Cramer’s Rule to determine this system: Finally, put D in and simplify 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 12
Example 1 Use Cramer’s Rule to determine this system: First, setup the Y solution 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 13
Example 1 Use Cramer’s Rule to determine this system: First, setup the Y solution To get Y, get rid of the coefficients in front of Y and replace them with the answers 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 14
Example 1 Use Cramer’s Rule to determine this system: Solve for Y. 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 15
Example 1 Use Cramer’s Rule to determine this system: Solve for Y. 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 16
Example 1 Use Cramer’s Rule to determine this system: Put D in and simplify 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 17
Example 1 Use Cramer’s Rule to determine this system: 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 18
Example 2 Use Cramer’s Rule to determine this system: 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 19
Your Turn Use Cramer’s Rule to determine this system: 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 20
Special Occurrences No Solution: Infinite Number of Solutions: 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 21
Example 3 Use Cramer’s Rule to determine this system: 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 22
Your Turn Use Cramer’s Rule to determine this system: 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 23
Example 4 On Monday, Angela babysat for 4 hours, did yard work for 2 hours, and earned a total of $41. On Friday, she babysat for 5 hours, did yard work for 3 hours, and earned a total of $65. Use Cramer’s Rule to determine the hourly rate for each activity. x = babysitting, y = yard work 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 24
Example 4 On Monday, Angela babysat for 4 hours, did yard work for 2 hours, and earned a total of $41. On Friday, she babysat for 5 hours, did yard work for 3 hours, and earned a total of $65. Use Cramer’s Rule to determine the hourly rate for each activity. 2/11/2022 3: 10 AM 3. 7 a - Cramer's Rule 25
Example 5 A nutritionist creates a diet for a long-distance runner that includes 3400 Calories from 680 grams of food, with half the Calories coming from carbohydrates. How many grams of protein, carbohydrates, and fat will this diet include? 4 p + 4 c + 9 f = 3400 p + c + f = 680 4 c = 1700 2/11/2022 3: 11 AM Equation for total Calories Total grams of food Calories from carbohydrates, 3. 7 a - Cramer's Rule 26
Example 5 A nutritionist creates a diet for a long-distance runner that includes 3400 Calories from 680 grams of food, with half the Calories coming from carbohydrates. How many grams of protein, carbohydrates, and fat will this diet include? p = 119 c = 725 f = 136 The diet includes 119 grams of protein, 425 grams of carbohydrates, and 136 grams of fat. 2/11/2022 3: 11 AM 3. 7 a - Cramer's Rule 27
Assignment Cramer’s Rule WKST 2/11/2022 3: 11 AM 3. 7 a - Cramer's Rule 28
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