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3.6 systems and matrices
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3.6 systems and matrices

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  • 1. 3.6 SOLVING SYSTEMS USING MATRICES
  • 2. MATRICES
    • A matrix is a rectangular array of numbers, displayed within brackets.
      • The dimensions of a matrix are the numbers of rows by the numbers of columns in the array.
  • 3. MATRICES
    • Each number in a matrix is a matrix element and can be identified by its row and column number
      • Example:
  • 4. EXAMPLE: IDENTIFYING A MATRIX ELEMENT
    • What is element in matrix A ?
  • 5. SYSTEMS OF EQUATIONS AND MATRICES
    • We can represent systems of equations as matrices
      • Each row represents an equation
      • Each column represents the coefficients of a variable
    • Example:
  • 6. REPRESENTING SYSTEMS WITH MATRICES
    • Stack the variables/constants
    • Write the matrix using coefficients and constants.
      • Use a 1 if there is no coeffiecient
      • Use a 0 if the variable is not included in the equation
  • 7. EXAMPLE: REPRESENT THE SYSTEM WITH A MATRIX
  • 8. EXAMPLE: WRITE THE SYSTEM OF EQUATIONS REPRESENTED BY THE MATRIX
  • 9. SOLVING A SYSTEM USING A MATRIX
    • We can solve a system by using a matrix and performing row operations
    • Row Operations are the “legal moves and manipulations” we can make in a matrix
    • Solving a system using row operations is similar to elimination, because we use the same steps, but don’t have variables
  • 10. SOLVING A SYSTEM USING MATRICES
    • Row Operations:
      • Switch any two rows
      • Multiply a row by a constant
      • Add one row to another row
  • 11. SOLVING A SYSTEM USING MATRICES
    • Goal: To use row operations to get a matrix in the following forms:
      • Matrices that represent the solution of a system are in reduced row echelon form .
  • 12. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX
  • 13. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX
  • 14. SOLVE THE SYSTEM OF EQUATIONS USING A MATRIX