Suppose A is a 4 x 3 matrix and b is a vector in R⁴ with the property that Ax has a unique solution. What can you say about the reduced echelon form of A? Justify your answer:
Choose the correct answer below:
a. The first term of the first row will be 1 and all other terms will be 0. There is only one variable Xₘ, so there is only one possible solution.
b. The first row will have a pivot position and the last row will be all zeros. If a row had more than one pivot position, then there would be an infinite number of solutions for aₘXₘ = bₘ.
c. There will be a pivot position in each row. If a row did not have a pivot position, then the equation Ax = b would be inconsistent.
d. The first row will have a pivot position and all other rows will be all zeros. There is only one equation to solve, so there is only one solution.
