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EvLer

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I am a bit confused with this problem:

Given AX = B, B != 0; X and Y satisfy the system. Find constants a and b such that aX + bY also satisfy the system.

The hint was: does (1/3)X+(2/3)Y work? Which would mean (1/3 + 2/3)(X + Y), which means X + Y. So, then I have X+Y as a potential solution, which is a solution? So, then does it mean that if a system has solutions, sum of those solutions is still a valid solution, but is any linear combination a solution? Then it would make a,b either such that a+b=1 or a,b any number.

Could someone explain, please?

Thank you very much.

Given AX = B, B != 0; X and Y satisfy the system. Find constants a and b such that aX + bY also satisfy the system.

The hint was: does (1/3)X+(2/3)Y work? Which would mean (1/3 + 2/3)(X + Y), which means X + Y. So, then I have X+Y as a potential solution, which is a solution? So, then does it mean that if a system has solutions, sum of those solutions is still a valid solution, but is any linear combination a solution? Then it would make a,b either such that a+b=1 or a,b any number.

Could someone explain, please?

Thank you very much.

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