 # Section 4-7 Augmented Matrices. Transform a system of equations into Row echelon form:

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Section 4-7 Augmented Matrices

Transform a system of equations into Row echelon form:

Coefficient Matrix Variable Matrix Constant Matrix 3x +4y -z = 12 (1) 7x -y +2z = -2 (2) 2x -2y -5z = 18 (3) 1.) Set up the matrix equation for the following equations =

The Augmented Matrix Def: The Augmented Matrix combines the coefficient matrix and the constant matrix. The variable matrix is omitted. 3 4 -1 12 7 -1 2 -2 2 -2 -5 18 When you enter this in your calculator you will not see the dashed line When you enter this in your calculator you will not see the dashed line Augmented matrix

Row operations: a.) Any 2 rows can be interchanged b.) Any row can be replaced with a multiple of that row c.) Any row can be replaced with the sum of that row and a multiple of another http://www.youtube.co m/watch?v=- aAucWVD--M

1 0 0 4 0 1 0 -3 0 0 1 1 System: 1x + 0y + 0z = 4 0x + 1y + 0z = -3 0x + 0y + 1z = 1 2.) The solution of a system of equations is x = 4, y = -3 and z = 1. Write this solution as an augmented matrix.

3. Solve the system of equations: a +2b +c = 0 2a +5b +4c = -1 a -b -9c = -5 Enter the augmented matrix into your calculator 1 2 1 0 2 5 4 -1 1 -1 -9 -5

Calculator steps to solve 2ndMatrix Math B: rref “reduced row echelon form” Enter 2ndMatrix Your home screen will show rref ( Arrow down to your augmented matrix Enter http://www.youtube.com/watch?v= wBmWsW26U7s&feature=relmfu

1 0 0 8 0 1 0 -5 0 0 1 2 x = 8 y = -5 z = 2 1 0 0 0 1 0 0 0 1 Coefficient Matrix xyzxyz = 8 -5 2 Variable Matrix = Constant Matrix Identity Matrix Identity Matrix Your home screen will show the resulting matrix Your home screen will show the resulting matrix 3.) (cont.) What does this augmented matrix represent?

Note: If you don’t wind up with the identity matrix then there is no solution

Homework Page 230 Problems: 12-25 all,

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