Alg II Unit 3-6-solvingsystemsmatrices

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Alg II Unit 3-6-solvingsystemsmatrices

  1. 1. 3-6 Solving SystemsUsing MatricesAlgebra II Unit 3 Linear Systems© Tentinger
  2. 2. Essential Understanding andObjectives• Essential Understanding: You can use a Matrix to represent and solve a system of equations without writing the variables.• Objectives:• Students will be able to: • Represent a system of linear equations with a matrix • Solve a system of equations using matrices
  3. 3. Iowa Core Curriculum• Algebra• A.REI.8 (+) Represent a system of linear equations as a single matrix equation in a vector variable.
  4. 4. Matrix• Matrix: a rectangular array of numbers. Displayed with brackets and the dimensions are the number of rows by the number of columns.• Dimensions: 2x3• Matrix Element: each number in the matrix. Represented by its row and column number as a subscript. For example in matrix A, a12 is the element in row 1 column 2 and is the fourth element.
  5. 5. Identify a Matrix Element.• A=• What is element a23 in matrix A?• What is element a13 in Matrix A• What is element a33 in matrix A?• What is element a24 in matrix A?
  6. 6. Representing a system ofequations with a matrix.• Each row represents an equation• Each column represents a variable, except the last column• The last column shows the constants to the right of the equal signs.• You only write the constant with the variable in the matrix• Draw a vertical bar to replace the equal signs• System Matrix
  7. 7. How can you represent the systemof equations with a matrix?
  8. 8. What linear system of equationsdoes the matrix represent?
  9. 9. Solving Systems• To solve a system of equations using matrices it should look like this when finished row reducing:• where x=a y=b z=c
  10. 10. Row operations:• Switch any two rows: Becomes• Multiply a row by a constant: Becomes• Add one row to another: Becomes• Combine any of these steps• Matrices that represent the solution of a system are in Reduced Row Echelon Form
  11. 11. Solving a system using amatrix• What is the solution of the system?
  12. 12. On the Calculator• Matrices that represent the solution of a system are in Reduced Row Echelon Form• Graphing Calculators will do the work for you using the rref function.• On the Calculator • Enter in the system into the matrix • Apply the rref() function to the matrix • List the solutions• What is the solution of the system of equations?
  13. 13. Homework• Pg 179-180• #8-14, 18 – 20, 24-26, 30, 34, 38• 15 problems

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