Question

If b does not equal 0​, can the solution set of ax = b be a plane through the​ origin?

Answer 1

If b does not equal 0​, can the solution set of ax = b be a plane through the​ origin

A plane pass through the origin mean it passes (0,0)

When we plug in 0 for x  then ax=b becomes

a(0) = 0 , when x = 0 then b not equal to 0 is a contradiction .

So , it is not possible if b does not equal 0​, can the solution set of ax = b be a plane through the​ origin.