A 1+b is linearly related to a2+b, that is, the two vectors are proportional.

There is a real number c that makes: a 1+b=c(a2+b).

Therefore: (a1+b)-(A2+B) = (c-1) (a2+b), which is still in direct proportion to a2+b and still related.

A 1 has nothing to do with the linearity of a2. For any real numbers c 1 and c2, there are: c 1a 1+c2a2≠0.

Substitute c 1= 1 and c2=- 1 to get: a 1-a2≠0.

concept

Linear algebra is a branch of algebra, which mainly deals with linear relations. Linear relationship means that the relationship between mathematical objects is expressed in linear form. For example, in analytic geometry, the equation of a straight line on the plane is a binary linear equation; The equation of spatial plane is a ternary linear equation, and the spatial straight line is regarded as the intersection of two planes, which is represented by an equation group composed of two ternary linear equations. A linear equation with n unknowns is called a linear equation.