rank of a 3rd matrix while appending columns of 2 matrices to the third matrix.

Question

A m×n is a matrix with rank r and B m×n is a matrix with rank r'. C is a matrix obtained from A by appending the columns of B. What can you say about the rank of C.

i am not getting how to go ahead with this question. please help me with the proof.

Answer 1

Hint: $\ A\ $ must have $\ r\ $ linearly independent columns, and $\ B\ $ must have $\ r'\ $. What is the minimum possible number of linearly independent columns $\ C $ can have? What is the maximum? Are all values between these two limits possible?