When you are solving a matix equation and the determinant of your coefficient matrix is zero, how can you determine when it is a no solution versus an infinitely many solution?

nvm i figured it out. you have to determine whether the system is consist or inconsistent.

Yes, you are correct! When solving a matrix equation and the determinant of the coefficient matrix is zero, you need to determine whether the system is consistent or inconsistent in order to determine if there is no solution or infinitely many solutions.

To do this, you can use several methods such as row reduction (Gaussian elimination), finding the rank of the matrix, or using the inverse of the coefficient matrix. The specific method may depend on the dimensions of the matrix equation.

If, after performing the necessary operations, you end up with a row of zeroes in the augmented matrix (representing an inconsistent system), then the system has no solution.

If you end up with a row of zeros and a non-zero value (representing a consistent system), then the system has infinitely many solutions.

Determining the consistency of a system can be a complex task, so it's important to carefully follow the steps and double-check your work to ensure accurate results.