Wednesday, April 17, 2019

College Algebra, Chapter 7, 7.1, Section 7.1, Problem 50

Find the complete solution of the system
{x3y+2z+w=2x2y2w=10z+5w=153x+2z+w=3


We transform the system into reduced row-echelon form

[1321212021000151530213]

R2R1R2

[132120123800151530213]

R43R1R4

[132120123800151509423]

R49R2R4

[132120123800151500142575]

R414R3R4

[132120123800151500045135]

145R4

[132120123800151500013]

R35R4R3

[13212012380010000013]

R2+3R4R2

[13212012010010000013]

R1R4R1

[13205012010010000013]

R2+2R3R2

[13205010010010000013]

R12R3R1

[13005010010010000013]

R1+3R2R1

[10002010010010000013]


We now have an equivalent matrix in reduced row-echelon form, and the system of equations is


{x=2y=1z=0w=3


We can write the solution as the ordered quadruple (2,1,0,3).

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