Solve the following system of equations using matrices (row operations). {−x+y+z=−1−x+5y−7z=−133x−2y−5z=0 Select one correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution is (_,_,_). B. There are infinitely many solutions. The solution can be written as {(x,y,z)∣x=,y=, z is any real number}. C. There are infinitely many solutions. The solution can be written as {x,y,z)∣x=, y is any real number, z is any real number}.

Question

Solve the following system of equations using matrices (row operations). {−x+y+z=−1−x+5y−7z=−133x−2y−5z=0 Select one correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution is (_,_,_). B. There are infinitely many solutions. The solution can be written as {(x,y,z)∣x=,y=, z is any real number}. C. There are infinitely many solutions. The solution can be written as {x,y,z)∣x=, y is any real number, z is any real number}.

Bertha Stark · Accepted Answer

Step 1 system Ax=b is [−111−15−73−2−5][xyz]=[−1−130] augmented matrix is [−111−1−15−7−133−2−50] Step 2 R1↔R3 [3−2−50−15−7−13−111−1] R2←R2+13⋅R1 R3←R3+13⋅R1 [3−2−500133−263−13013−23−1] R3←R3−113⋅R2 =[3−2−500133−263−130000] R2←313⋅R2 =[3−2−5001−2−30000] R1←R1+2⋅R2 [30−9−601−2−30000] R1←13⋅R1 =[10−3−201−2−30000] reduced system is [10−301−2000][xyz]=[−2−30] x−3z=−2………………..x−−2+3z

Solve the following system of equations using matrices (row operations).

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