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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 Row-Echelon form when ones are on the main diagonal, and zeros are in the bottom left corner. Systems in Row-Echelon 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 Row-Echelon 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 non-zero constant 3. Add a multiple of one row to another row....
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