MATH 1324 Quiz 12 Show all work in the space provided. Credit will be given only
ID: 3113947 • Letter: M
Question
MATH 1324
Quiz 12
Show all work in the space provided. Credit will be given only for work that is clear and readable.
1. Let A= [ 3 -4 0 B= [0 -4 C=[1 -2 D=[7 1
1 x 2 ] -2 3 5 7] -3 0]
1 y]
. Perform the indicated operations
a) 2C-3D
a) __________________
b) AB
b) __________________
c) BA
c) __________________
d) AC
d) __________________
2. A company makes gizmos, gadgets, and widgets. Each gizmo requires 3 hours of painting, 4 hours of trimming and 1 hour of packaging to produce. Each gadget requires 2 hours of painting, 5 hours of trimming and 2 hours of packaging. Each widget requires 4 hours of painting, 2 hours of trimming, and 3 hours of packaging. Form a 3X3 matrix, H, summarizing this information as follows.
The company has plants in Louisiana and New Jersey. In Louisiana, the paint shop pays $9/hr., the trim shop pays $8.50/hr., and the packing shop pays $7.25/hr. In New Jersey, the paint shop pays $9.50 /hr., the trim shop pays $9/hr., and the packing shop pays $8.38/hr. Summarize this information in a matrix W, such that the product HW is doable mathematically and makes sense within the context of the problem.
Compute the matrix HW and interpret each entry.
3. A decorator wants to purchase plants for a new home. She is interested in three types of plants costing $7, $10, and $13 each. If she has budgeted exactly $150 for the plants and wants to purchase exactly 15 of them, what are her options? List or make a chart of ALL options.
Explanation / Answer
1. a. 2C-3D
2C= 2 [ 1 -2 = [2 -4
5 7] 10 14]
3D = 3[7 1 = [21 3
-3 0] -9 0 ]
2C-3D = [2 -4 - [21 3 = [2-21 -4-3 = [-19 -7
10 14] -9 0] 10-(-9) 14-0] 19 14]
B. AB
A= [3 -4 0 B = [0 -4
1 x 2] -2 3
1 y]
AB = [3*0+-4*-2+0*1 3*-4+-4*3+0*y = [8 -24
1*0+x*-2+2*1 1*-4+x*3+2*y] -2x+2 -4+3x+2y]
BA=
B= [0 -4 A= [3 -4 0
-2 3 1 x 2]
1 y]
BA = [0*3+-4*1 0*-4+-4*x 0*0+-4*2 = [ 4 -4x -8
-2*3+3*1 -2*-4+3*x -2*0+3*2 -3 8+3x 6
1*3+y*1 1*-4+y*x 1*0+y*2] 3+y -4+xy 2y]
AC=
A= [3 -4 0 C = [1 -2
1 x 2] 5 7]
AC= not possible. number of column of the 1st matrix must be equal to the number of the rows of the 2nd matrix.
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