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Matrices on the TI

Matrices on the TI. Use the 2 nd MATRIX button to access matrix operations NAMES recalls the value of a previously stored matrix into a formula MATH lists functions to perform Especially interested in det (determinant) and rref (reduced row echelon form)

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Matrices on the TI

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  1. Matrices on the TI • Use the 2nd MATRIX button to access matrix operations • NAMES recalls the value of a previously stored matrix into a formula • MATH lists functions to perform • Especially interested in det (determinant) and rref (reduced row echelon form) • EDIT is used to enter/change matrix contents • The calculator doesn’t store answers: You need to use the STO > button to store results into matrix names. • It helps to write down these names so you remember what they are • For Cramer’s Rule (§7.4), you can store the values of determinants (which are just numbers) in individual number variables using the ALPHA key and letter names: A, B, C, etc.

  2. Matrix Multiplication:§7.4 Example 10, pg 508A Good Example of Why Matrix Multiplication Makes Sense All matrices classify how one characteristic of a situation is effected by another. This is true even in geometric or other abstract situations. “Materials” is effected by “Cost”: A unit of concrete costs $20 “Model” is effected by “Style”: 20 Y’s are to be made in the Ranch style “Style” is effected by “Materials”: A ranch is made up of 50 units of concrete $ Colonial Ranch Concrete Lumber Brick Shingles Concrete Lumber Brick Shingles Model X Model Y Model Z Colonial Ranch Multiplication links up a chain of effects: (Model vs. Style) × (Style vs. Materials) × (Materials vs. Cost) = (Model vs.Cost)

  3. Enter into the TI using 2nd MATRIX, EDIT NAMES MATH EDIT 1: [A] 2: [B] 3: [C] 4: [D] 5: [E] 6 ↓ [F] EDIT MATRIX [A] 3 X 2 [0 30 ] [10 20 ] [20 20 ] 3,2=20 1: ENTER 20 2nd MATRIX, EDIT: NAMES MATH EDIT 1: [A] 3X2 2: [B] 3: [C] 4: [D] 5: [E] 6 ↓ [F] EDIT MATRIX [B] 2 X 4 _2 0 2 ] _1 20 2 ] 2,4=2 2: 2 ENTER

  4. 2nd MATRIX, EDIT: NAMES MATH EDIT 1: [A] 3X2 2: [B] 2X4 3: [C] 4: [D] 5: [E] 6 ↓ [F] EDIT MATRIX [C] 4 X 1 [20 ] [180 ] [60 ] [25 ] 4,1=25 ENTER 3: 25 2nd QUIT

  5. We can also do a “Total” matrix which gives the total number of each Model (for question (b) of the Example): Model X Model Y Model Z Total 2nd MATRIX, EDIT: NAMES MATH EDIT 1: [A] 3X2 2: [B] 2X4 3: [C] 4X1 4: [D] 5: [E] 6 ↓ [F] EDIT MATRIX [F] 1 X 3 [ 1 1 1 ] 1,3=1 1 ENTER 6: 2nd QUIT

  6. (a) What is the total cost of materials for all houses of each model? (Model vs.Cost) = (Model vs. Style) × (Style vs. Materials) × (Materials vs. Cost) = A B C NAMES MATH EDIT 1: [A] 3X2 2: [B] 2X4 3: [C] 4X1 4: [D] 5: [E] 6 ↓ [F] 1X3 NAMES [A]* 1: 2nd MATRIX, NAMES: ENTER, × NAMES MATH EDIT 1: [A] 3X2 2: [B] 2X4 3: [C] 4X1 4: [D] 5: [E] 6 ↓ [F] 1X3 [A]*[B]* NAMES 2nd MATRIX, NAMES: ENTER, × 2:

  7. NAMES MATH EDIT 1: [A] 3X2 2: [B] 2X4 3: [C] 4X1 4: [D] 5: [E] 6 ↓ [F] 1X3 NAMES [A]*[B]*[C] [ [72900] [54700] [60800] ] ENTER, ENTER 2nd MATRIX, NAMES: 3: $ Model X Model Y Model Z

  8. (b) How much of each of the four kinds of material must be ordered? (Model vs.Materials) = (Model vs. Style) × (Style vs. Materials) = A B [A]*[B] [ [1500 30 600 6… [1100 40 400 6… [1200 60 400 8… [A]*[B] …500 30 600 60] …100 40 400 60] …200 60 400 80]] STO >, 2nd MATRIX, NAMES, [E] [A]*[B] [ [1500 30 600 6… [1100 40 400 6… [1200 60 400 8… Ans→[E] [ [1500 30 600 6… [1100 40 400 6… [1200 60 400 8… Concrete Lumber Brick Shingles Model X Model Y Model Z

  9. The totals can be found by multiplying by the (Total vs. Model) matrix Concrete Lumber Brick Shingles Model X Model Y Model Z Model X Model Y Model Z Total [F]*[E] [ [3800 130 1400 200] ] Concrete Lumber Brick Shingles Total

  10. (c) Find the total cost of the materials (Total vs. Cost) = (Total vs. Materials) × (Materials vs. Cost) [F]*[E] [ [3800 130 1400 200] ] Ans*[C] [ [188400] ] 2nd ANS $ Total

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