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Apply the Gaussian elimination method on the following augmented matrix. Determine the rank and nullity of the coefficient matrix. Determine the basic and free variables and find the solution. 2 1 -8 1 -2 -3 1 -1 1 2 3

Apply the Gaussian elimination method on the following augmented matrix. Determine the rank and nullity of the coefficient matrix. Determine the basic and free variables and find the solution. 2 1 -8 1 -2 -3 1 -1 1 2 3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Apply the Gaussian elimination method on the following augmented matrix. Determine the rank and nullity of the coefficient matrix. Determine the basic and free variables and find the solution. -8 -2 -3 1 -1 1 2
Transcribed Image Text:Apply the Gaussian elimination method on the following augmented matrix. Determine the rank and nullity of the coefficient matrix. Determine the basic and free variables and find the solution. -8 -2 -3 1 -1 1 2
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Given augmented matrix        02101-2-3 1  -1120 -803  ~ 1-2-31021 0  -1120 0-83     R2→R2↔R1 ~ 1-2-31021 0  0-1-11 0-83     R3→R3+R1 ~ 1-2-31021 0  0101 0-8-5     R3→R3+R2 Now the system of linear equation can begiven as   x1-2x2-3x3+x4=0   — 1                                    2x2+x3=-8 —2                                     x2+x4=-5  —3Put x2=t , then from 3 we get x4=-5-t                            from 2 we get x3=-8-2tThen from 1 x1-2t-3(-8-2t) + -5-t = 0                                    ⇒x1=-19-3t

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