Saturday, May 4, 2013

College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 8

Find the complete solution of the system
{xy+z=2x+y+3z=62y+3z=5
using Gaussian Elimination.

For this system we have

[111211360235]

R2R1R2

[111202240235]

12R2

[111201120235]

R32R2R3

[111201120011]

Now we have equivalent matrix in row-echelon form and the corresponding system is


{xy+z=2y+z=2z=1


Then we back-substitute z=1 into the second equation and solve for y


y+1=2Back-substitute z=1y=1Subtract 1


Now we back-substitute y=1 and z=1 into the first equation and solve for x


x1+1=2Back-substitute y=1 and z=1x=2Simplify

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