Period+8+-+Determinants

Michael BL Evan Reiff Vincent Wang

Determinant of a 2 x 2 (3 8) (4 5) (3 8) ---\--- (4 5) (3 8) ---/--- (4 5) (3*5) - (8*4) = Determinant Determinant = -25
 * Data can usually be summarized in a table
 * If the titles of the columns and the rows are known though, the table can be further summarized as a matrix
 * || Burgers || French Fries ||
 * Evan || 3 || 8 ||
 * Mike || 4 || 5 ||
 * This is a matrix, specifically a 2x2
 * All 2x2 matrices will then each have its own "determinant value"
 * The determinant can be used to calculate solutions for system of equations.
 * In a 2x2 matrix, the determinant is found by subtracting the product of the numbers of the secondary diagonal from the products of the numbers of the primary diagonal
 * Primary diagonal is the top-left number to the bottom-right number
 * Secondary diagonal is simply the other diagonal, the top-right number to the bottom-left one.
 * The determinant is the primary diagonal subtracting the secondary diagonal

(12 7) (9 22)
 * Try this problem - find the determinant of this matrix - use the program to help if you are having trouble



You need to apply these methods in Cramer's Rule for a 2x2 system: http://hmaricca.wikispaces.com/Period+8+Cramer%27s+Rule+for+a+2x2+System

Determinant of a 3 x 3

General Form:
 * a1 || b1 || c1 ||
 * a2 || b2 || c2 ||
 * a3 || b3 || c3 ||

General form of the Determinant- a1b2c3+a2b3c1+a3b1c2- (a3b2c1+a1b3c2+a2b1c3)

Example: First add the first two columns to the table.
 * || vanilla || choclate || strawberry ||
 * Mike || 3 || 2 || 4 ||
 * Evan || 1 || 8 || 9 ||
 * Vincent || 3 || 1 || 5 ||

Now add the products of the primary diagonals 1- 3x8x5= 120 2- 2x9x3= 54 3 4x1x1= __4__ sume 178
 * 3 || 2 || 4 || 3 || 2 ||
 * 1 || 8 || 9 || 1 || 8 ||
 * 3 || 1 || 5 || 3 || 1 ||

Next the sum of the 3 secondary diagonals. 1- 4x8x3= 96 2- 3x9x1= 27 3- 2x1x5= __10__ 133

The determinant is (the sum of the products of the primary diagonal)- (the sum of the products of the secondary diagonal) 178-133= =45



You need to apply these methods in Cramer's Rule for a 3x3 system: http://hmaricca.wikispaces.com/Cramer%27s+Rule+for+a+3x3+System

Bibliography + Extra Materials:

2x2 http://www.wisc-online.com/Objects/ViewObject.aspx?ID=TMH1501

3x3 http://www.wisc-online.com/objects/ViewObject.aspx?ID=TMH1602