4.3 Worksheet Evaluate the determinant. 1. −3 4
= 7 5
2. 12 −1
= 4 2
Use Matrices to solve the system of equations. x + y − z = −3
1. 2. 3. 2x − 3y + 4z = 23 −3x + y − 2z = −15
3x + 3y + 4z = 1
3x + 5y + 9z = 2 5x + 9y + 17z = 4
5x + 3y − 2z = −4
2x + 2y + 2z = 0 3x + 2y + 1z = 1
4. 2x − 4y + 5z = −33
4x − y = −5
−2x + 2y − 3z = 19
Applications: 1. Claire and Dale shopped at the same store. Claire bought 5 kg of apples and 2 kg of bananas and paid altogether $22. Dale bought 4 kg of apples and 6 kg of bananas and paid altogether $33. Use matrices to find the cost of 1 kg of bananas. 2. Ann and Billy both entered a quiz. The quiz had twenty questions and points were allocated as follows: § P points were added for each correctly answered question § Q points were deducted for each incorrect (or unanswered) question Ann got 15 questions correct and scored 65 points. Billy got 11 questions correct and scored 37 points. Use matrices to find the value of Q. 3. A community relief fund receives a large donation of $2800. The foundation agrees to spend the money on $20 school bags, $25 sweaters, and $5 notebooks. They want to buy 200 items and send them to schools in earthquake-­‐hit areas. They must order as many notebooks as school bags and sweaters combined. How many of each item should they order? 4. An ultimate Frisbee team has to order jerseys, shorts, and hats. They have a budget of $1350 to spend on $50 jerseys, $20 shorts, and $15 hats. They want to buy 40 items in preparation for the oncoming season and must order as many jerseys as shorts and hats combined. How many of each item should they order?