Friday, January 22, 2016

College Algebra, Chapter 7, 7.1, Section 7.1, Problem 44

Find the complete solution of the system

{3x+y=24x+3y+z=42x+5y+z=0


We transform the system into row-echelon form

[310243142510]

13R1

[11302343142510]

R2+4R1R2

[113023013312032510]

R32R1R3

[113023013312030133143]

313R2

[1130230131320130133143]

R3133R2R3

[1130230131320130008]

18R3

[1130230131320130001]

This last matrix is in row-echelon form, so we stop the Gaussian Elimination Process. Now if we translate the last row back into equation form, we get 0x+0y+0z=1 or 0=1, which is false. This means that the system has no solution or it is inconsistent.

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