alg ii unit 3-6-solvingsystemsmatrices
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3-6 Solving Systems Using MatricesAlgebra II Unit 3 Linear Systems
© Tentinger
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Essential Understanding and Objectives
• 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
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Iowa Core Curriculum
• Algebra
• A.REI.8 (+) Represent a system of linear equations as a single matrix equation in a vector variable.
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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.
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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?
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Representing a system of equations 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
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How can you represent the system of equations with a matrix?
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What linear system of equations does the matrix represent?
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Solving Systems
• To solve a system of equations using matrices it should look like this when finished row reducing:
• where x = ay = bz = c
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Row operations:• Switch any two rows:
• Multiply a row by a constant:
• Add one row to another:
• Combine any of these steps
• Matrices that represent the solution of a system are in Reduced Row Echelon Form
Becomes
Becomes
Becomes
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Solving a system using a matrix• What is the solution of the system?
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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 rreffunction.
• 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?
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Homework
• Pg 179-180
• #8-14, 18 – 20, 24-26, 30, 34, 38
• 15 problems