Section 12: Calculating with Matrices 157
Week
1 2 3
Total Weight (kg) 274
233
331
Total Value $120.32
$112.96
$151.36
Silas knows that he received $0.24 per kilogram for his cabbage and $0.86
per kilogram for his broccoli. Use matrix operations to determine the
weights of cabbage and broccoli he delivered each week.
Solution: Each week’s delivery represents two linear equations (one for
weight and one for value) with two unknown variables (the weights of
cabbage and broccoli). All three weeks can be handled simultaneously
using the matrix equation
1 1
0.24 0.86
d
11
d
12
d
13
d
21
d
22
d
23
=
274 233 331
120.32 112.96 151.36
or
AD = B
where the first row of matrix D is the weights of cabbage for the three
weeks and the second row is the weights of broccoli.
Keystrokes Display
2 v ´ m A
2.0000
Dimensions A as 2 × 2
matrix.
´ > 1
2.0000
Sets row and column
numbers in R
and R
to 1.
´ U
2.0000
Activates User mode.
1 O A
1.0000
Stores a
11
.
O A
1.0000
Stores a
12
.
.24 O A
0.2400
Stores a
21
.
.86 O A
0.8600
Stores a
22
.
2 v 3 ´ m B
3.0000
Dimensions B as 2 × 3
matrix.
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