Lecture 5 Gauss Elimination PDF
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This document presents a lecture on the Gauss elimination method for solving systems of linear equations. The example problems demonstrates how to use augmented matrices to eliminate variables and find solutions.
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Lecture 5 Gauss Elimination Solve the following systems by Gaussian elimination 𝒙 − 𝟐𝒚 + 𝟑𝒛 = 𝟗 , −𝒙 + 𝟑𝒚 = −𝟒 , 𝟐𝒙 − 𝟓𝒚 + 𝟓𝒛 = 𝟏𝟕 Solution Augmented Matrix 𝟏 −𝟐 𝟑 𝟗 −𝟏 𝟑 𝟎 −𝟒...
Lecture 5 Gauss Elimination Solve the following systems by Gaussian elimination 𝒙 − 𝟐𝒚 + 𝟑𝒛 = 𝟗 , −𝒙 + 𝟑𝒚 = −𝟒 , 𝟐𝒙 − 𝟓𝒚 + 𝟓𝒛 = 𝟏𝟕 Solution Augmented Matrix 𝟏 −𝟐 𝟑 𝟗 −𝟏 𝟑 𝟎 −𝟒 𝟐 −𝟓 𝟓 𝟏𝟕 Lecture 5 Gauss Elimination Solve the following systems by Gaussian elimination 𝒙 − 𝟐𝒚 + 𝟑𝒛 = 𝟗 , −𝒙 + 𝟑𝒚 = −𝟒 , 𝟐𝒙 − 𝟓𝒚 + 𝟓𝒛 = 𝟏𝟕 Solution Augmented Matrix 𝟏 −𝟐 𝟑 𝟗 −𝟏 𝟑 𝟎 −𝟒 𝟐 −𝟓 𝟓 𝟏𝟕 𝑅1 +𝑅2 =𝑅2 1 −2 3 9 0 1 3 5 2 −5 5 17 −2𝑅1 +𝑅3 =𝑅3 1 −2 3 9 0 1 3 5 0 −1 −1 −1 𝑅2 +𝑅3 =𝑅3 1 −2 3 9 0 1 3 5 0 0 2 4 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑡ℎ𝑖𝑟𝑑 𝑟𝑜𝑤 2𝑧 = 4 → 𝑧 = 2 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑠𝑒𝑐𝑜𝑛𝑑 𝑟𝑜𝑤 𝑦 + 3𝑧 = 5 → 𝑦 + 6 = 5 𝑦 = −1 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑟𝑜𝑤 𝒙 − 𝟐𝒚 + 𝟑𝒛 = 𝟗 𝑥+2+6=9 𝑥=1
