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Linear Algebra and also Its Applications, 5th Edition

Authors: David C. Lay, Steven R. Lay, Judi J. McDonald

ISBN-13: 978-0321982384

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See our systems for question 1E from thing 1.5 indigenous Lay's linear Algebra and Its Applications, fifth Edition.

You are watching: Determine if the system has a nontrivial solution. try to use as few row operations as possible.

Chapter:1.11.21.31.41.51.61.71.81.91.101.SE2.12.22.32.42.52.62.72.82.92.SE3.13.23.33.SE4.14.24.34.44.54.64.74.84.94.SE5.15.25.35.45.55.65.75.85.SE6.16.26.36.46.56.66.76.86.SE7.17.27.37.47.57.SE8.18.28.38.48.58.6
Problem:1E2E3E4E5E6E7E8E9E10E11E12E13E14E15E16E17E18E19E20E21E22E23E24E25E26E27E28E29E30E31E32E33E34E35E36E37E38E39E40E
In exercises 1-4, identify if the system has a nontrivial solution. Shot to usage as couple of row operations together possible...
Step 1 of 2

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Step 2 that 2

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Step 1Given device of Equations: \<\beginarrayl2x_1 - 5x_2 + 8x_3 = 0\\ - 2x_1 - 7x_2 + x_3 = 0\\4x_1 + 2x_2 + 7x_3 = 0\endarray\>We have to determine if the system has a nontrivial solution. Step 2: The Augmented Form\\>Step 3: lessened Echelon Form\<\beginarraylM = \left< \beginarray*20c2& - 5&8&0\\ - 2& - 7&1&0\\4&2&7&0\endarray \right>\\\\ = \left< \beginarray*20c2& - 5&8&0\\0& - 12&9&0\\0&12& - 9&0\endarray \right>\,\,\,\left\ R_3 = R_3 - 2R_1;\,\,R_2 = R_2 + R_1 \right\\\\\ = \left< \beginarray*20c2& - 5&8&0\\0& - 12&9&0\\0&0&0&0\endarray \right>\,\,\,\left\ R_3 = R_3 + R_2 \right\\endarray\>Step 4: general SolutionFrom the diminished echelon form, we can see the the critical row has actually all 0 entries, making one totally free variable. If over there is any complimentary variable in system of equation, the system, has actually a no trivial solution.ANSWER NON-TRIVAL SOLUTION