vela said:The presence of a 1 on the RHS isn't a problem. You're trying to solve an inhomogeneous system, so a constant term in the solution is expected.
What equations did you get after you reduced them?
Mark44 said:Since this is a nonhomogeneous system (as vela points out), you should be working with an augmented matrix with 3 rows and 6 columns. The sixth column will have the constants.
In Z2 refers to the set of integers modulo 2, which includes only the numbers 0 and 1. Finding all the solutions means determining all the possible values for the given equation or problem within this set.
Problems that involve equations with integer coefficients and a finite number of solutions can be solved using In Z2. This includes problems in algebra, number theory, and cryptography.
The solution set in Z2 is limited to only the values 0 and 1, while the solution set in the set of integers includes all positive and negative integers. Additionally, in Z2 the operations of addition and multiplication are performed modulo 2, meaning that any result greater than 1 is reduced to either 0 or 1.
Solving problems in Z2 can have real-world applications in fields such as computer science, coding theory, and engineering. It can also help to develop critical thinking and problem-solving skills.
The process involves setting up and solving equations using the rules of arithmetic in Z2, including performing operations modulo 2. The solutions are then found by determining all possible values for the variables within the given equation or problem.