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Unformatted text preview: Section 6.1 – Matrix Solutions to Linear Systems If a matrix has M rows and N columns, then it is called an M × N matrix. Matrix elements are denoted: a ij ie, element a 24 is in row 2, column 4 Solving Linear Systems Using Matrices: Example : Write the augmented matrix for each of the following systems: a) = = + 1 3 10 5 2 y x y x b)  = + = = + + 10 4 4 3 2 1 z y z x z y x c) Write the system that corresponds to this augmented matrix: 2 3 6 1 4 1 7 3 9 A matrix is in RowEchelon form when ones are on the main diagonal, and zeros are in the bottom left “corner”. Systems in RowEchelon form can be solved using back substitution . Example : Solve the following: 1 2 4 5 1 2 3 1 3 1 A matrix is in Reduced RowEchelon form when ones are on the main diagonal, and zeros are in the bottom left and top right corners. Example : 1 6 1 4 1 13 Performing Matrix Row Operations (Gaussian Elimination): The following are the legal operations: 1. Swap two rows 2. Multiply a row by a nonzero constant 3. Add a multiple of one row to another row....
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 Spring '12
 LisaJuliano
 Gaussian Elimination, Linear Systems, Matrices, a2 b2 c2

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