precalc unit 6 sys of eqs and matrices.notebook
TRANSCRIPT
PreCalc Unit 6 Sys of Eqs and Matrices.notebook
1
January 17, 2019
Jul 2612:02 PM
Okay, lets' try that again!Write each system of equations in triangular form using Gaussian elimination. Then solve the system.
x + 2y 3z = 28 3x + 5y + 8z = 20
3x y + 2z = 3 x + 2y 4z = 18
x + y z = 5 6x + 4z = 0
Jul 2612:02 PM
Okay, lets' try that again!Write each system of equations in triangular form using Gaussian elimination. Then solve the system.
x + 2y 3z = 28 3x + 5y + 8z = 20
3x y + 2z = 3 x + 2y 4z = 18
x + y z = 5 6x + 4z = 0
PreCalc Unit 6 Sys of Eqs and Matrices.notebook
2
January 17, 2019
Aug 119:28 PM
Write the augmented matrix for each system of linear equations:4w 5x + 7z = 11 3w + 7x + y = 21
w + 8x + 3y = 6 4w 12y + 8z = 5
15x 2y + 10z = 9 16w 14y + z = 2
w + x + 2y = 7
Jul 2612:02 PM
Now, let's try this system...
w/Gaussian Elimination...
in an augmented Matrix
PreCalc Unit 6 Sys of Eqs and Matrices.notebook
3
January 17, 2019
Jul 2612:02 PM
Once we put our system in an augmented matrix, we can produce an equivalent augmented matrix using elementary row operations (b/c the operations are simple to perform, but easy to make mistakes on):• interchange any two rows• multiply one row by a nonzero real number• add a multiple of one row to another row
If one matrix can be obtained by a sequence of row operations on another, the 2 matrices are said to be row equivalent
Jul 2612:02 PM
(first nonzero entry in a row is 1, called a leading 1)
Identify an Augmented Matrix in Row Echelon form:1 2 0 | 1 1 6 2 | 1 1 0 0 | 19 0 1 0 4 | 10
0 1 4 | 2 0 0 0 | 0 0 1 0 | 4 1 0 3 10 | 7
0 1 3 | 9 0 0 1 | 20 0 1 6 0 | 8
0 0 1 2 | 4
PreCalc Unit 6 Sys of Eqs and Matrices.notebook
4
January 17, 2019
Jul 2612:02 PM
Gaussian Elimination with a MatrixTRAVEL Manuel went to Italy for Spring Break last year. This year, he wants to go to France. The average hotel, food, and transportation costs for each city in France that he wants to visit are shown. Write and solve a system of equations to determine how many days Manuel spent in each city. Interpret your solution.
(once you get to row echelon form, substitute and solve but, if you get a false equation, your systems has no solution)
Jul 2612:02 PM
Reduced rowechelon form is unique, unlike rowechelon form, b/c you can perform a variety of operations in a variety of ways, but the solution is the solution and it is unique.
PreCalc Unit 6 Sys of Eqs and Matrices.notebook
5
January 17, 2019
Jul 2612:02 PM
Solve each system of equations.x y + z = 0 x + 2y 3z = 7 4x + 9y + 16z = 2
x + 2y 3z = 5 3x 7y +9z = 12 x 2y 4z = 1
2x 3y + 5z = 8 2x + y 5z = 8 2x + 4y + 9z = 5
Jul 2612:02 PM
If you can't write your matrix in reduced rowechelon form, the system either has no solution or infinitely many solutions
Solve Each System of Equations
3x y 5z = 9 x + 3y + 4z = 8
4x + 2y 3z = 6 4x 2y z = 6
7x 11y 3z = 3 8x 18y 19z = 2