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Published byJuliana Farmer Modified over 6 years ago

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Section 4-7 Augmented Matrices

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Transform a system of equations into Row echelon form:

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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 =

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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

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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

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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.

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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

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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

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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?

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

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Homework Page 230 Problems: 12-25 all,

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