Is the zero vector a linear combination of any nonempty set of vectors?

Question: Is the zero vector a linear combination of any nonempty set of vectors ? Justify. Is the set of all differential real valued functions defined on R...

Does ax = bx imply a = b in any vector space?justify

Question: Does ax = bx imply a = b in any vector space? Justify. Let v = $${(a_1, a_2):a_1, a_2 \in f}$$ where f is field. Define addition of elements of v c...

The Power of ‘Why not?’

Introduction What if I did this? What if I couldn’t do this?  (a + b)^2 = a^2 + 2ab + b^2 (a - b)^2 = a^2 - 2ab + b^2