Find the range space and rank of each map What is the set an

Find the range space and rank of each map.

What is the set and why is the rank one? Please explain and show steps.

Solution

The range space

R(h) = {a + d | a, b, c, d R}

is all of R (we can get any real number by taking d to be 0 and taking a to be the desired number). Thus, the rank is one.