Algebra I : Semester II : Solving Systems

Sections:

Introduction  |   Section 1  |   Section 2  |   Section 3  |  Section 4  |  Section 5

Section Four

Part 1  |  Part 2  |  Part 3

Algebra 1 : Section 4: Solving Systems Addition of Matrices Andy Garrett and Leo Bradley are each managing two different farm operations. Below is the table for their operations in 2004 and 2005. The numbers stand for the numbers of acres harvested during the year. Farm 2004 2005   Corn Wheat Oats Corn Wheat Oats Garrett 1304 2050 1820 1838 1910 1630 Bradley 1256 1925 1750 2030 2005 1800 Example 1:  Writing Matrices Write two matrices for the information, using the 2004 data for matrix A and the 2005 data for matrix B.  Use Garrett and Bradley for the rows and the type of crop for the columns. The matrix for 2004: The matrix for 2005:   Think About It How could you find the totals for each crop, in each farm, over the two years, using matrices A and B? The easiest way is to add each element in matrix A to the element in the same position in matrix B. The sum would be:   To Add or Subtract Matrices The matrices must have the same dimensions Add (or subtract) each element in the first matrix to the element in the same position in the second matrix. Example 2: Add or Subtract the Matrices as Indicated A + B A – B A + C It is not possible to add A + C is not possible. The two matrices must have the same dimensions. C + D C – D   Quick Practice The two matrices that represented the Garrett and Bradley farms were:      The matrix for 2004: The matrix for 2005: Find out how many more acres were planted for each crop in 2004. You can find the answer by finding B – A.  A negative number represents a drop in acres planted for that crop and farm. The Fresh Market (a small grocery business) keeps a weekly log of the cost of items ordered in each of its two stores. The table below represents the cost of items ordered over a two-week period. Create two matrices, Q and R, to represent the costs for Week 1 and Week 2.   Week 1 Week 2 Store Fresh Produce Canned or Boxed Food Frozen Food Fresh Produce Canned or Boxed Food Frozen Food Store A $4,500 $6,715 $8,249 $3,920 $7,210 $6,521 Store B $5,640 $6,432 $7,841 $5,890 $5,989 $8,258 Matrices Q and R: Find Q + R.  What does this represent? The sum of Q + R represents the total costs for Week 1 and Week 2 for each item at each store. Find R – Q.  What does this represent? The difference of R – Q represents the increase or decrease in cost for each item at each store. Now go on to the next part

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