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
Iowa Core Curriculum• Algebra• A.REI.8 (+) Represent a system of linear equations as a single matrix equation in a vector variable.
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.
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?
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
How can you represent the systemof equations with a matrix?
What linear system of equationsdoes the matrix represent?
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
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
Solving a system using amatrix• What is the solution of the system?
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?