To solve a matrix system with equations involving a^2 - 1, a, and b, you can use the method of substitution. First, solve for one variable in one equation and then plug that value into the other equations to solve for the remaining variables.
Yes, Gaussian elimination can also be used to solve a matrix system with equations involving a^2 - 1, a, and b. You will need to perform the same operations as you would for a regular matrix system, such as row operations and back substitution.
If the matrix system has more than 3 variables, including a^2 - 1, a, and b, you will need to use a variation of the substitution and/or Gaussian elimination method. You may also need to use additional techniques such as Cramer's rule or the inverse matrix method.
To check if your solution to the matrix system is correct, you can substitute the values you found for the variables into each equation and see if they satisfy all of the equations. If they do, then your solution is correct.
Yes, there are some special cases that may arise when solving a matrix system with equations involving a^2 - 1, a, and b. For example, if any of the equations are inconsistent or dependent, the system may have no solution or infinite solutions. It is important to carefully analyze the system and equations to determine if there are any special cases.