Answer :
Final answer:
In Gaussian elimination, a system of 3000 equations in 3000 unknowns can be solved in 5 seconds on a given computer. Therefore, the number of back substitutions that can be done per second is 0.2.
Explanation:
In Gaussian elimination, for each equation you perform a series of row operations to eliminate variables and solve for one variable at a time. Back substitution is then used to find the values of the remaining variables. Since the system of 3000 equations in 3000 unknowns can be solved in 5 seconds, we can calculate the speed at which back substitutions can be done per second.
- Gaussian elimination requires n^3/3 arithmetic operations, where n is the number of unknowns.
- The time complexity of Gaussian elimination is O(n^3).
- Since the number of unknowns is 3000 and the system can be solved in 5 seconds, the time it takes to perform one Gaussian elimination is 5 seconds.
- Therefore, the number of back substitutions that can be done per second is 1/5 = 0.2.
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