2. Algebra 2 13.3a Niagara Falls

3. Get ready for a “Small Quiz” to be written on your grade sheet.

4. Quiz. Copy the problems and write the answer. Put your grade paper on the front of your row, quiz side down. 1. Solve using substitution: 2. Solve using elimination:

5. A rectangular array of numbers is called a matrix. Example: This is a 2×3 matrix (2 rows and 3 columns). Every square matrix is associated with a number called its determinant. The determinant of matrix A is denoted, (not absolute value). Definition: The determinant of matrix is: (You start at the upper left, just like reading a book.)

6. 1.Evaluate: 2.Evaluate: 3.Evaluate: 4.Evaluate:

7. Solve using Cramer’s Rule To solve using Cramer’s Rule, we need one more determinant than we have equations. The first determinant is called the denominator determinant, and it is made from the coefficients of x and y. Example: If we solve then the denominator determinant To find x, we replace the numbers on the right side of each equation with the numbers in the x column. So the numerator determinant for x is So the value of x is

8. In the same way, in making the numerator determinant, we replace the y column with the answer column: The value of y is So the answer is (1, 4). In summary, to find the solution to a system of equations by using Cramer’s Rule, we find:.

9. Three equations: If we have three equations with 3 unknowns, we find.

10. You work:

12. Classwork: 2, 10/580