This is a Linear Algerbra question Can a set of two vectors

This is a Linear Algerbra question.

Can a set of two vectors span all of R^3. If yes, give an example. If not, explain why not.

Solution

For spanning any Rⁿ plane there should be a vector or component of the vector along the dimensions . But , when we have two vectors , the plane can be obtained with the help of linear combination of the two vectora but the third dimension would be left out . Hence , there is a minimum requirement of three vectors to span R³ . Therefore , set of two vectors cannot span R³