Math 121 discussion - Gaussian elimination

# Math 121 discussion - Gaussian elimination - MATH 121 EXTRA...

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MATH 121 EXTRA PRACTICE PROBLEMS: WEEK 1-3 (1) When presented with a system of equations with 3 or more equations, we should solve it using Gaussian elimination . It is convenient to rewrite the system as an augmented matrix with the coeﬃcient matrix on the left, a vertical line, and then the constants on the right of the vertical line. Ax + By + Cz = D Ex + Fy + Gz = H Ix + Jy + Kz = L A B C D E F G H I J K L Remark: If a variable is absent from an equation, it is represented by a ”0” in our aug- mented matrix. Similarly, if we have a ”0” in our augmented matrix, the corresponding linear equation does not have that variable. (2) We wish to transform the augmented matrix to one that has a coeﬃcient matrix that is upper triangular (i.e. it has all 1’s in the diagonal and 0’s below the diagonal). Note: In this guide, the ?’s denote coeﬃcients and constants in our matrix. A B C D E F G H I J K L 1 ? ? ? 0 1 ? ? 0 0 1

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## This note was uploaded on 12/07/2010 for the course MATH Math 121 taught by Professor Beaulieu during the Fall '10 term at UMass (Amherst).

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Math 121 discussion - Gaussian elimination - MATH 121 EXTRA...

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