Chapter 3 7 Determinants Cramers Rule 23 A

Chapter 3. 7 Determinants & Cramer’s Rule #23 A man has one hundred dollars and you leave him with two dollars. That's subtraction. ~Mae West

From 3. 1 to 3. 6 • We have been solving systems of equation that evolve 3 variables • We have been solving systems that only have two variables. – Substitution – Elimination – Graphing – NOW Determinants

Determinants Every square matrix has a real number associated with it. This number is used when finding inverses and solving linear systems. 2 x 2 Determinant (det A or |A|)

Determinants Every square matrix has a real number associated with it. This number is used when finding inverses and solving linear systems. 2 x 2 Determinant (det A or |A|)

Determinants Every square matrix has a real number associated with it. This number is used when finding inverses and solving linear systems. 2 x 2 Determinant (det A or |A|)

3 x 3 Determinants 1. 2. 3. 4. Copy the first two columns at the end of the matrix. Multiply down and add Multiply up & add Subtract result of step #4 from result of step #3

Example:

Now why? ? • We are going to use these to solve systems with 2 equations and two unknowns first we need to change the equation in to an matrix

Cramer’s Rule Note Card! Linear systems can be solved using matrices by using this rule. 1. Find the determinant of the Linear System Coefficient Matrix coefficient matrix. (If this is 0 the problem cannot be solved) 2. Solve for x 3. Solve for y

a b e Solve: 1. Find det. of the Coeff. Matrix 2. Solve for x 3. Solve for y c d f Coefficient Matrix

Assignment • p 207 7 -13, 29 -31