Show all work and steps clearly. Use the following matrices for problems 1 – 4. If it cannot be done, state so and give the reason why it cannot be done. If it can be done, simplify as much as possible.
A= [ 3x 2 ] B= [ 2 x ] C= [ -1 2 ] D= [ x -1 ]
[ -4 1 ] [ 3 -1 ] [ -4 1 ] [ 2 5 ]
[ 3 y+1 ] [ y 4]
1. AB= ?
2. AC= ?
5. The Mundo Candy Company makes three types of chocolate candy: Cheery Cherry, Mucho Mocha, and Almond Delight. The company produces its products in San Diego, Mexico City and Managua using two main ingredients: Chocolate and sugar. Each kg of Cheery Cherry requires 0.5 kg of sugar and 0.2 kg of chocolate; each kg of Mucho Mocha requires 0.4 kg of sugar and 0.3 kg of chocolate, and each kg of Almond Delight requires 0.3 kg of sugar and 0.3 kg of chocolate. The cost of 1 kg of sugar is $4 in San Diego, $2 in Mexico City, and $1 in Managua. The cost of 1 kg of chocolate is $3 in San Diego, $5 in Mexico City, and $7 in Managua.
a) Create a 2X3 matrix, A, that gives the relationship between the types of candy and their component ingredients. Label all rows and columns using proper units.
b) Create a 3X2 matrix, C, that gives each ingredient cost in each city. Label all rows and columns using proper units.
c) To get the cost of ingredients for each type of candy, do you need to evaluate AC or CA?
d) Evaluate your answer to c) being sure to label each row and column. Write a sentence for each entry that tells me exactly what that number in the matrix represents. Remember to use proper units.
6. Solve using the Gauss-Jordan method. Circle your pivots. Show the new matrix after every pivot and write out all row operations in the order that they must be done.