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Ax=b1 and Ax=b2 are consistent. Is the system Ax=b1+b2 necessarily consistent? 
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#1
Nov2012, 09:30 PM

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1. The problem statement, all variables and given/known data
Suppose A is m*n matrix b1 and b2 are m*1 vector and the systems Ax=b1 and Ax=b2 are consistent. Is the system Ax=b1+b2 necessarily consistent? 2. Relevant equations 3. The attempt at a solution I think Ax = b1 + b2 should be consistent but i dont know how to prove.. 


#2
Nov2012, 09:37 PM

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#3
Nov2012, 09:59 PM

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So Ax1+Ax2=b1+b2=A(x1+x2) so (x1+x2)could be x prove ? Is this correct ? 


#4
Nov2012, 10:03 PM

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Ax=b1 and Ax=b2 are consistent. Is the system Ax=b1+b2 necessarily consistent?



#5
Nov2012, 10:19 PM

P: 22

Anyway thanks for the help 


#6
Nov2012, 10:22 PM

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