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How can you identify a dependent or inconsistent system by looking at an augmented matrix in reduced row echelon form?
I bet it can be done, but I'll be darned if I can!
What is the identity matrix?
The identity matrix is a square one with ones (1s) down its main diagonal and zeroes (0s) elsewhere. That is, it must have the same number of rows as columns, and where the row number is the same as the column number, the entry must be 1, elsewhere, it must be 0.
How to construct a matrix with 23 elements?
It will either be a 1*23 row matrix or a 23*1 column matrix.
Does doing row operations on a matrix change its determinant?
No.
Calculating the complexity of determinant of matrix with n columns?
Using the method derived from the usual definition using the minors, the complexity is O(n!). But it seems that one could just do the Gaussian elimination on the matrix, turning the matrix into a triangular one while keeping track of any neccessary row swaps, and then just multiply the values of the diagona. This method would get the complexity of O(n*n).
