Unit 7, Lesson 4 Trigonometry / Pre-Calculus

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Presentation transcript:

Unit 7, Lesson 4 Trigonometry / Pre-Calculus Matrices and Systems of Equations

Solve the system of equations Do Now

Solve the system of equations Do Now

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Instead of stopping with row-echelon form, you could continue the process to “reduced row-echelon” form, which is triangular, with zeros after the variables, as in the next example. Matrices Wilhelm Jordan

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

So how do you get this on your calculator? Catalog button Matrices

5 m-by-n matrix Matrices

Enter the right numbers for the size of the matrix Matrices

Enter the values in the matrix Matrices

The function rref() is for reduced row echelon form Matrices

How to complete on a TI-84 Use the 2nd MATRIX button to define a matrix, remember the letter assigned to your matrix Matrices

Use the 2nd CATALOG button to find the function rref(), use the alpha keys to move to letters quicker rref( Matrices

Add the matrix name after the parenthesis, with the matrix button again rref([A]) Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

Matrices

(3,5,1) Solve the system of equations x – y + 5z = 3 x + 2y – 6z = 7 Matrices

(-10,5,-2) Solve the system of equations 11x + 22y – 11z = 22 Matrices

(-37,12,-5) Solve the system of equations 6x + 18y – 6z = 24 Matrices

Inconsistent Solve the system of equations x – 8y + 4z = 11 Matrices

(7k-4,4k+1,k) Solve the system of equations -5x – 10y + 75z = 10 – x + 7z = 4 x + y – 11z = – 3 (7k-4,4k+1,k) Matrices

Solve the system of equations x + 2y – 4z – 5w = 14 x + 3y – 4z – 5w = 21 2x + 2y – 8z – 10w = 14 (4m+5n,7,m,n) Matrices

Matrices

Matrices

Matrices

Matrices

Homework Page 499 – 503 7,9,11,17,23-27 35, 41, 61, 63, 65, 75, 80 Matrices

a. b. c. Do Now

a. b. c. Do Now