Find the complete solution of the system
{−4x−y+36z=24x−2y+9z=3−2x+y+6z=6
We first write the augmented matrix of the system and using Gauss-Jordan Elimination.
[−4−136241−293−2166]
−14R1
[114−9−61−293−2166]
R3+2R1→R3
[114−9−61−293032−12−6]
23R3
[114−9−61−29301−8−4]
R2−R1→R2
[114−9−60−9418901−8−4]
−49R2
[114−9−601−8−401−8−4]
R3−R2→R3
[114−9−601−8−40000]
R1−14R2→R1
[10−7−501−8−40000]
This is in reduced row-echelon form since the last row represents the equation 0=0, we may discard it. So the last matrix corresponds to the system
{x−7z=−5y−8z=−4
To obtain the complete solution, we solve for the leading variables x and y in terms of the nonleading variable z and we let z be any real numbers. Thus, the complete solution is
x=7t−5y=8t−4z=t
where t is any real number.
No comments:
Post a Comment