Suppose that a doesn't equal 0.
a) If a.b = a.c, does it follow that b = c?
b) If axb = axc does it follow that b = c?
c) If a.b = a.c and axb = axc, does it follow that b = c?
look at this website:
www.math.ucla.edu/~ronmiech/Calculus_Problems/32A/chap11/section4/709d39/709_39.html
I don't under even after looking at the site.
a) In the equation a.b = a.c, since a is nonzero, we can divide both sides of the equation by a to get b = c. Therefore, it follows that b = c.
b) In the equation axb = axc, we know that a is nonzero. However, we cannot divide both sides of the equation by a, as we would like to cancel out the "a". This is because multiplication is not an invertible operation, meaning we cannot always undo it by dividing. Therefore, we cannot conclude that b = c in this case.
c) To determine if b = c, we need to analyze both equations together. From the equation a.b = a.c, we have established that b = c. However, from the equation axb = axc, we cannot conclude that b = c as explained earlier. Therefore, with the given information, we cannot guarantee that b = c.