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System and Matrixes Chapter 3

System and Matrixes Chapter 3. By Kate Hanna, Danielle Pomante , Nasheeba St. Louis. Elimination Eliminate the y. Times Eq. 3 by 2. Eliminate y in Eq. 2&3 Solve new system. Add new equations. Put into original equation & solve for y. 16x+11z=-1 -16x-7z=-11 4z=-12

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System and Matrixes Chapter 3

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  1. System and MatrixesChapter 3 By Kate Hanna, Danielle Pomante, Nasheeba St. Louis

  2. EliminationEliminate the y. Times Eq. 3 by 2.Eliminate y in Eq. 2&3Solve new system. Add new equations.Put into original equation & solve for y. 16x+11z=-1 -16x-7z=-11 4z=-12 z=-3 16x+11(-3)=-2 x=2 6x-y+4z=-1 6(2)-y+4(-3)=-1 y=1 x=2, y=1, z=-3 Ordered triple=(2,1,-3)  4x+2y+3z=1     2x-3y+5z=-14     6x-y+4z=-1      4x+2y+3z=1 +12x-2y+8z=-2     16x+11z=-1      2x-3y+5z=-14 -18x+3y-12z=3       -16x-7z=-11

  3. Example 1: elimination Page 182 # 11 3x – y + 2z = 4 6x – 2y + 4z = -8 2x – y + 3z = 10

  4. Substitution x + y + z = 4 x + y - z = -4 3x + 3y + z = 12 • Make one equation equal to one variable.  x + y + z = 4 x= -y - z + 4 • Then plug x into the equation

  5. Example 2: Page 182 # 17 4x + y + 5z = -40 -3x + 2y + 4z = 10 X – y – 2z = -2

  6. Graphing 3 Variable Equations 3x + 4y + 12z • Find the intercept of each variable 3(0) + 4(0) + 6z = 12 6z=12          z=2                        Point:  (0, 0, 2) 3(0) + 4y + 6(0) = 12  4y = 12       y=3                        Point: (0, 3, 0)      3x + 4(0) + 6(0) = 12       3x = 12       x=4                        Point: (4, 0, 0) • Plot each point on 3-axis graph.

  7. Example 3: Page 177 # 6 2x + 9y – 3z = -18 z y x

  8. Adding & Subtracting Matrixes

  9. Multiplying Matrixes

  10. Example 4: Page 196 example 2

  11. Inverse Matrixes On your calculator: 2nd Matrixes  Edit  1: [A], etc Enter Numbers  Inverse A-1 = 2nd, X-1

  12. Practice Problems ! Solve 2 Variable Equations – p 156 Graph Systems of Linear Equations – p 171 Solve 3 Variable Equations – p 182-183 Basic Matrixes – p 191 Multiplying Matrixes – p 199-200 Inverse – p 214

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