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# Lect2 - Math1111 Systems of Linear Equations Methodology...

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Unformatted text preview: Math1111 Systems of Linear Equations Methodology Locate the 1st column containing a nonzero entry Pick a row with a nonzero entry to be pivotal row Perform row operations to eliminate other entries in the column Repeat the steps to the remaining smaller matrix. Math1111 Systems of Linear Equations Methodology Locate the 1st column containing a nonzero entry Pick a row with a nonzero entry to be pivotal row Perform row operations to eliminate other entries in the column Repeat the steps to the remaining smaller matrix.       1 2 1 3 3- 1- 3- 1 2 3 1 4       Math1111 Systems of Linear Equations Methodology Locate the 1st column containing a nonzero entry Pick a row with a nonzero entry to be pivotal row Perform row operations to eliminate other entries in the column Repeat the steps to the remaining smaller matrix.       1 2 1 3 3- 1- 3- 1 2 3 1 4       Math1111 Systems of Linear Equations Methodology Locate the 1st column containing a nonzero entry Pick a row with a nonzero entry to be pivotal row Perform row operations to eliminate other entries in the column Repeat the steps to the remaining smaller matrix.       1 2 1 3 3- 1- 3- 1 2 3 1 4      -→       1 2 1 3- 7- 6- 10- 1- 1- 2       Math1111 Systems of Linear Equations Methodology Locate the 1st column containing a nonzero entry Pick a row with a nonzero entry to be pivotal row Perform row operations to eliminate other entries in the column Repeat the steps to the remaining smaller matrix.       1 2 1 3 3- 1- 3- 1 2 3 1 4      -→       1 2 1 3- 7- 6- 10- 1- 1- 2       Math1111 Systems of Linear Equations Methodology Locate the 1st column containing a nonzero entry Pick a row with a nonzero entry to be pivotal row Perform row operations to eliminate other entries in the column Repeat the steps to the remaining smaller matrix.       1 2 1 3 3- 1- 3- 1 2 3 1 4      -→       1 2 1 3- 7- 6- 10- 1- 1- 2      -→       1 2 1 3- 7- 6- 10- 1 7- 4 7       Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve           - x 2- x 3 + x 4 = x 1 + x 2 + x 3 + x 4 = 6 2 x 1 + 4 x 2 + x 3- 2 x 4 =- 1 3 x 1 + x 2- 2 x 3 + 2 x 4 = 3 Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve           - x 2- x 3 + x 4 = x 1 + x 2 + x 3 + x 4 = 6 2 x 1 + 4 x 2 + x 3- 2 x 4 =- 1 3 x 1 + x 2- 2 x 3 + 2 x 4 = 3 Solution . The augmented matrix is         - 1- 1 1 1 1 1 1 2 4 1- 2 3 1- 2 2 6- 1 3          Math1111 Systems of Linear Equations Elementary Row Operations - Example Example . Solve     ...
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Lect2 - Math1111 Systems of Linear Equations Methodology...

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