For the given systems of linear equations, determine the values of b_1, b_2, text{ and } b_3 necessary for the system to be consistent. (Using matrices) x-y+3z=b_1 3x-3y+9z=b_2 -2x+2y-6z=b_3

he298c 2020-12-25 Answered
For the given systems of linear equations, determine the values of b1,b2, and b3 necessary for the system to be consistent. (Using matrices)
xy+3z=b1
3x3y+9z=b2
2x+2y6z=b3
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Expert Answer

oppturf
Answered 2020-12-26 Author has 94 answers
Step 1
Consider
xy+3z=b1
3x3y+az=b2
2x+2y6z=b3
[The system Ax=b is cosistent if Rank(A)=Rank(A|b)]
[A|b]=[113|b1339|b2226|b3]
R2R23R1,R3R3+2R1
[A|b][113|b1000|b23b1000|b3+2b1]
the Rank(A) will be equal to Rank(A|b) iff b23b1=0 and b3+2b1=0
which implies b2=3b1
and b3=2b1
Hence , given system will be consistent iff b={[b13b12b1]|b1R}
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Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

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