Final answer:
The columns of B span R4 if and only if the equation Bx = y has a solution for each y in R4. To determine if the columns of B span R4, we can check if the rank of B is equal to 4.
Step-by-step explanation:
The columns of B span R4 if and only if the equation Bx = y has a solution for each y in R4. To determine if the columns of B span R4, we can check if the rank of B is equal to 4. If the rank of B is 4, then the columns of B span R4 and the equation Bx = y has a solution for each y in R4. If the rank of B is less than 4, then the columns of B do not span R4 and the equation Bx = y may not have a solution for every y in R4.