A bakery sells three types ofcakes, each requiring the amounts of the basic ingredients shown in the following matrix.

Type of Cake

Ingredient I II III

Flour (in cups) 2 6 4

Sugar (in cups) 2 1 2

Eggs 2 1 3

To fill its daily orders for these three kinds ofcakes, the bakery uses 120 cups offlour, 52 cups ofsugar, and 66 eggs. Complete parts(a) through(c) below.

(a) please write a 3 1 matrix for the amounts used daily.

(b) Let the number of daily orders for cakes be a 31 matrix X with entries x1, x2, and x3. Please write a equation that can

be solved for X, using the given matrix and the matrix from part (a).

(c) Solve the equation from part (b) to find the number of daily orders for each type of cake.