3.6 SOLVING SYSTEMSUSING MATRICES
MATRICES   A matrix is a rectangular array of numbers,    displayed within brackets.               2 4 1              A...
MATRICES   Each number in a matrix is a matrix element    and can be identified by its row and column    number     Exam...
EXAMPLE: IDENTIFYING AMATRIX ELEMENTWhat is element a23 in matrix A?    4 −9 17        1   A= 0 5 8           6      ...
SYSTEMS OF EQUATIONS ANDMATRICES   We can represent systems of equations as matrices     Each row represents an equation...
REPRESENTING SYSTEMSWITH MATRICES
EXAMPLE: REPRESENT THESYSTEM WITH A MATRIXx − 3y + z = 6 x + 3 z = 12 y = −5 x + 1
EXAMPLE: WRITE THE SYSTEMOF EQUATIONS REPRESENTEDBY THE MATRIX5 2 7       0 1 9 
SOLVING A SYSTEM USING AMATRIX   We can solve a system by using a matrix and    performing row operations   Row Operatio...
SOLVING A SYSTEM USINGMATRICES   Row Operations:     Switch any two rows     Multiply a row by a constant     Add (sub...
SOLVING A SYSTEM USINGMATRICES Goal:To use row operations to get a matrix in the following forms:                        ...
SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX x + 4 y = −12 x + 5 y = 4
SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX9 x − 2 y = 53 x + 7 y = 17
SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX x + 2 y = 163 x + y = 8
ASSIGNMENT Page 179 #8 – 11, 13 – 23 odd, 24, 27 – 29
3.6 SOLVING SYSTEMSUSING MATRICESPart 2 – Three- Variable Systems
USING MATRICES FOR THREEVARIABLE SYSTEMS   Same goal and row operations used to solve a    system with two variables
SOLVING A SYSTEM USINGMATRICES   Row Operations:     Switch any two rows     Multiply a row by a constant     Add (sub...
SOLVING A SYSTEM USINGMATRICES Goal:To use row operations to get a matrix in the following forms:                        ...
SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX
SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX
SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX
ASSIGNMENT   3.6 Worksheet
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3.6 systems and matrices[1]

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3.6 systems and matrices[1]

  1. 1. 3.6 SOLVING SYSTEMSUSING MATRICES
  2. 2. MATRICES A matrix is a rectangular array of numbers, displayed within brackets. 2 4 1  A=  6 5 3   The dimensions of a matrix are the numbers of rows by the numbers of columns in the array.
  3. 3. MATRICES Each number in a matrix is a matrix element and can be identified by its row and column number  Example:  a11 a12 a13  A=  a21 a22 a23  
  4. 4. EXAMPLE: IDENTIFYING AMATRIX ELEMENTWhat is element a23 in matrix A?  4 −9 17 1 A= 0 5 8 6     −3 −2 10  0  
  5. 5. SYSTEMS OF EQUATIONS ANDMATRICES We can represent systems of equations as matrices  Each row represents an equation  Each column represents the coefficients of a variable Example:
  6. 6. REPRESENTING SYSTEMSWITH MATRICES
  7. 7. EXAMPLE: REPRESENT THESYSTEM WITH A MATRIXx − 3y + z = 6 x + 3 z = 12 y = −5 x + 1
  8. 8. EXAMPLE: WRITE THE SYSTEMOF EQUATIONS REPRESENTEDBY THE MATRIX5 2 7  0 1 9 
  9. 9. SOLVING A SYSTEM USING AMATRIX 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. 10. SOLVING A SYSTEM USINGMATRICES Row Operations:  Switch any two rows  Multiply a row by a constant  Add (subtract) one row to another row Make sure you write down what you are doing!
  11. 11. SOLVING A SYSTEM USINGMATRICES Goal:To use row operations to get a matrix in the following forms: 1 0 0 a  1 0 a      or 0 1 0 b  0 1 b  0 0 1 c     Matricesthat represent the solution of a system are in reduced row echelon form.
  12. 12. SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX x + 4 y = −12 x + 5 y = 4
  13. 13. SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX9 x − 2 y = 53 x + 7 y = 17
  14. 14. SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX x + 2 y = 163 x + y = 8
  15. 15. ASSIGNMENT Page 179 #8 – 11, 13 – 23 odd, 24, 27 – 29
  16. 16. 3.6 SOLVING SYSTEMSUSING MATRICESPart 2 – Three- Variable Systems
  17. 17. USING MATRICES FOR THREEVARIABLE SYSTEMS Same goal and row operations used to solve a system with two variables
  18. 18. SOLVING A SYSTEM USINGMATRICES Row Operations:  Switch any two rows  Multiply a row by a constant  Add (subtract) one row to another row Make sure you write down what you are doing!
  19. 19. SOLVING A SYSTEM USINGMATRICES Goal:To use row operations to get a matrix in the following forms: 1 0 0 a  1 0 a      or 0 1 0 b  0 1 b  0 0 1 c     Matricesthat represent the solution of a system are in reduced row echelon form.
  20. 20. SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX
  21. 21. SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX
  22. 22. SOLVE THE SYSTEM OFEQUATIONS USING A MATRIX
  23. 23. ASSIGNMENT 3.6 Worksheet

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