A Set Having a Unique Solution
Determine whether the following set has a unique solution, and if so, find it:
3x – 2y + 8z = 48 –
9x + 4y + 2z = 24
»rank ([A b))
Because A and [A b] have the same rank, a solution exists. Because this rank equals the number of unknowns (which is three), the solution is unique. The left-division method gives this solution, which is x = 2, y = -1, z = 5.