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Exercise 14 - Matrix Consistency

If the system Anxnx = b1 and Anxny = b2 are consistent. Does that mean Ax = b1 + b2 is consistent. Justify?

Answer:
Now there exist x1 such that Ax1=b1 and there exist x2 such that Ax2=b2.
So A(x1+x2)= Ax1+Ax2=b1+b2
Therefore, Ax =b1+b2 is consistent.

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